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Quizzes > High School Quizzes > Electives

Practice Quiz: Which Statement About This System is True?

Sharpen your skills with equations and expressions.

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting The Equation Truth Challenge quiz for high school students.

Evaluate the equation 2 + 3 = 5. Is it true?
True
Depends on context
False
Insufficient information
The equation 2 + 3 equals 5, which is a basic arithmetic fact. This confirms the statement is true in all standard numeric contexts.
Determine if the equation 4 Ã - 2 = 8 is correct.
None of the above
False
True
Only sometimes
Multiplying 4 by 2 results in 8, making the equation valid. This reinforces a fundamental multiplication fact.
If x = 3, does the equation x + 2 = 5 hold true?
No
It depends on x
Not enough information
Yes
Substituting x = 3 into the equation gives 3 + 2 = 5, which is correct. This simple substitution confirms the equation holds true.
Is the equation 10 âˆ' 4 = 6 valid?
It might be true
Yes
No
Only in certain cases
Since 10 minus 4 equals 6, the statement is accurate. This is a straightforward subtraction problem demonstrating basic arithmetic skills.
Evaluate the statement: 7 = 7. Is it accurate?
Yes
Sometimes true
Only when compared to another number
No
The equation 7 = 7 is always true because both sides are identical. It is an example of an equality that holds under all circumstances.
Determine if the equation 3(x âˆ' 2) = 3x âˆ' 6 is true for all values of x.
True only when x = -2
False for all values of x
True for all values of x
True only when x = 2
Expanding the left side using the distributive property gives 3x âˆ' 6, which is identical to the right side. This shows the equation holds true for every value of x.
Which property is used to simplify the equation 3(x + 4) = 3x + 12?
Identity Property
Distributive Property
Commutative Property
Associative Property
The distributive property allows multiplication to be applied over addition, expanding 3(x + 4) into 3x + 12. This is a foundational technique in algebra.
Solve for x in the equation 5x = 20.
x = 5
x = 20
x = 0
x = 4
Dividing both sides by 5 yields x = 20/5, which simplifies to x = 4. This is a basic example of solving a linear equation.
Solve for x in the equation x/2 = 3.
x = 1.5
x = 3
x = 6
x = 9
Multiplying both sides by 2 gives x = 3 Ã - 2, resulting in x = 6. This demonstrates a simple method for solving equations with fractions.
Find the value of x that satisfies the equation x + 5 = 12.
x = 17
x = 7
x = -7
x = 5
Subtracting 5 from both sides results in x = 12 âˆ' 5, which simplifies to x = 7. This is a straightforward application of inverse operations.
Evaluate if the equation 2x âˆ' 1 = x + 3 is true when x equals 4.
It is true only for x = 3
It cannot be determined
No, it is false
Yes, it is true
Substituting x = 4 gives 2(4) âˆ' 1 = 8 âˆ' 1 = 7 and 4 + 3 = 7, so both sides are equal. This confirms the equation holds true for x = 4.
Determine if the equation 4(x âˆ' 3) = 4x âˆ' 12 is an identity.
Yes, it is an identity
No, it is contradictory
No, it is conditional
It is true only for x = 3
Expanding the left side yields 4x âˆ' 12, which exactly matches the right side. This shows that the equation is an identity, true for every value of x.
Determine the type of solution for the equation 3x + 2 = 2x + 5.
Infinitely many solutions
No solution
Dependent on x
A unique solution
Subtracting 2x from both sides gives x + 2 = 5, and then subtracting 2 results in x = 3. Since only one value of x satisfies the equation, it has a unique solution.
Verify if the equation 8 âˆ' 2x = 2(4 âˆ' x) holds true for all values of x.
Yes, it is valid for all x
Only true when x = 2
False for all x
Valid only when x = 4
Expanding the right side results in 8 âˆ' 2x, which is identical to the left side. This confirms that the equation is an identity valid for every value of x.
Determine the truth value of the equation 0x = 0.
Never true
No solution
True only when x = 0
Always true
Since 0 multiplied by any number is 0, the equation 0x = 0 holds for all values of x. This represents an identity in algebra.
Determine if the system of equations {2x + 3y = 6, 4x + 6y = 12} has one solution, no solution, or infinitely many solutions.
Infinitely many solutions
One unique solution
Depends on the values of x and y
No solution
The second equation is exactly two times the first, meaning both represent the same line. Hence, the system has infinitely many solutions since every solution of the first equation satisfies the second.
For the system {x + y = 5, x âˆ' y = 1}, identify the correct pair (x, y) that satisfies both equations.
(1, 4)
(3, 2)
(2, 3)
(4, 1)
By adding the two equations, we get 2x = 6, so x = 3. Substituting x into one of the equations gives y = 2. Therefore, the pair (3, 2) is the unique solution for the system.
Assess the truth of the statement: 'If two equations in a system are multiples of each other, the system must have infinitely many solutions.'
False
It depends on the constant terms
True
It may have no solution
When one equation is a multiple of another, they represent the same line (assuming no inconsistency in constants). Thus, any solution of one equation automatically satisfies the other, giving infinitely many solutions.
Evaluate the following process: 'Starting with the equation 2(x + 3) = 2x + 3, distributing gives 2x + 6 = 2x + 3, which simplifies to 6 = 3, indicating no solution.' Is this process accurate?
No, the process is incorrect because distribution was applied wrong
The process is partly correct but leads to a unique solution
No, the original equation has infinitely many solutions
Yes, the process is accurate and the equation has no solution
Correctly distributing 2 over (x + 3) results in 2x + 6, and equating it to 2x + 3 leads to the false statement 6 = 3. This contradiction proves that the equation is inconsistent and has no solution.
Given the system {x + 2y = 4, 2x + 4y = 8}, assess the validity of the statement: 'Adding a redundant equation to a system does not affect its solution set.'
True
It depends on the method used
False
Only in linear systems
Since 2x + 4y = 8 is a multiple of x + 2y = 4, it provides no new information about the variables. Therefore, adding it to the system does not change the original solution set.
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Study Outcomes

  1. Understand how to evaluate the accuracy of algebraic equations.
  2. Analyze algebraic expressions for logical and mathematical consistency.
  3. Apply problem-solving strategies to verify the truthfulness of equations.
  4. Synthesize algebraic principles to identify and correct errors in equations.
  5. Demonstrate improved exam readiness through systematic equation analysis.

Equations Quiz: True Statements Challenge Cheat Sheet

  1. Understand the different methods for solving systems of equations - Exploring graphing, substitution, and elimination helps you choose the most efficient path to the solution. Graphing gives a visual grasp, substitution is perfect for isolating variables, and elimination shines when you can neatly cancel terms. OpenStax Algebra Key Concepts
  2. Recognize consistent vs. inconsistent systems - A consistent system has at least one solution, while an inconsistent system has none. Spotting these characteristics early prevents wasted effort and guides your choice of methods. Wikipedia: Consistent & Inconsistent Equations
  3. Learn the FOIL method for multiplying binomials - FOIL stands for First, Outer, Inner, Last, and it's a quick way to expand expressions like (x + 2)(x - 3). Mastering FOIL lets you tackle polynomial multiplication confidently. Online Math Learning: Algebra Mnemonics
  4. Memorize the order of operations (PEMDAS) - PEMDAS stands for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction and ensures you evaluate expressions correctly every time. Mixing up the sequence can lead to mistakes, so keep this acronym handy. Wikipedia: List of Mnemonics
  5. Practice solving systems by graphing - Plot each equation on the same coordinate plane, draw the lines accurately, and look for their intersection point. This visual method reinforces your understanding of how solutions emerge geometrically. OpenStax Algebra Key Concepts
  6. Master the substitution method - Solve one equation for a variable (like y = 2x + 3), then plug that expression into the other equation. This turns a two-variable system into a single-variable problem you can tackle directly. OpenStax Algebra Key Concepts
  7. Utilize the elimination method - Add or subtract equations to cancel out one variable, leaving a simpler equation to solve. Once one variable is found, back‑substitute to get the other. OpenStax Algebra Key Concepts
  8. Understand slope-intercept form - In y = mx + b, m is the slope and b is the y‑intercept, so you can graph a line in two quick steps: start at (0, b) and use slope m. This form also helps compare different linear models. Online Math Learning: Algebra Mnemonics
  9. Use mnemonic devices to remember rules - Clever phrases like "All Cows Eat Grass" help lock in multi-step processes, such as the substitution method or the FOIL order. Creating your own mnemonics turns dry rules into memorable bites. LastMinRead: Math Mnemonics
  10. Regularly practice different systems - Speed and confidence come from variety: mix linear, fractional, and word‑problem systems in your drills. Consistent practice builds intuition, so you'll recognize patterns and pick methods instinctively. Miracle Math: Memorisation Strategies
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