Systems of Linear Equations Unit Test

Question

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Question
Use the image to answer the question.

A coordinate plane with four quadrants shows the x-axis ranging from negative 10 to 10 in increments of 1 and the y-axis ranging from negative 5 to 15 in increments of 1. A solid line and a dotted line intersect each other. The equation of the solid line is y equals 4 x minus 10. The equation of the dotted line is y equals negative 2 x plus 8. The intersection point of both lines is shown at positive 3 on the x-axis and positive 2 on the y-axis in quadrant 1.

Review the graphs of a system of these two linear equations in two variables: y=4x−10
and y=−2x+8
Find the solution of the system.

(1 point)
The solution of the system of equations is (
).

Answer 1

The solution to the system of equations is the point where the two lines intersect. From your description, the two equations given are:

1. \( y = 4x - 10 \)
2. \( y = -2x + 8 \)

You mentioned that the intersection point is at \( (3, 2) \).

To confirm this, we can substitute \( x = 3 \) into both equations:

1. For the first equation: \( y = 4(3) - 10 = 12 - 10 = 2 \)

2. For the second equation: \( y = -2(3) + 8 = -6 + 8 = 2 \)

Both equations yield \( y = 2 \) when \( x = 3 \), confirming that the point \( (3, 2) \) is indeed the solution.

Therefore, the solution of the system of equations is:

\((3, 2)\)