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Question

Difficulty: EasySystems of Linear Equations
A system of linear equations is shown below.
y=2x−7y = 2x - 7
3x−2y=113x - 2y = 11

What is the value of xx?

  1. A
    8
  2. B
    -25
  3. 3Answer
  4. D
    -3

Answer

The correct value of xx is 3.
The correct value of xx is 3, which is found by substituting 2x−72x - 7 for yy in the second equation and solving for xx.

Step-by-Step Solution

1
Substitute the expression for yy from the first equation into the second equation.
3x−2(2x−7)=113x - 2(2x - 7) = 11
Since the first equation defines yy in terms of xx, substitution is a direct way to eliminate yy and solve for xx.
2
Distribute the −2-2 to both terms inside the parentheses.
3x−4x+14=113x - 4x + 14 = 11
Applying the distributive property requires multiplying −2-2 by both 2x2x and −7-7, remembering that negative times negative is positive.
3
Combine the like terms on the left side of the equation.
−x+14=11-x + 14 = 11
Simplifying the expression by combining the xx terms (3x−4x=−x3x - 4x = -x).
4
Isolate the variable term by subtracting 14 from both sides.
−x=−3-x = -3
Using the subtraction property of equality to move the constant term to the right side.
5
Solve for xx by multiplying or dividing both sides by −1-1.
x=3x = 3
Finding the positive value of xx.

Key Concept

Solving systems of linear equations using the substitution method.
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Topics

Systems of Linear Equations

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