Solving Systems of Equations by Graphing Practice

Question

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4 of 54 of 5 Items

Question
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An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 10 to 10 in increments of 1. A solid line and a dotted line with arrows at both the ends intersect each other. The equation of the solid line is y equals negative x plus 6. The equation of the dotted line is y equals x plus 2. The lines intersect at left parenthesis 2 comma 4 right parenthesis which is not plotted as a point.

Estimate the intersection point of the graphs of the following linear equations in two variables.
y=x+2


y=−x+6


(1 point)
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])

Answer 1

To find the intersection point of the lines given by the equations \( y = x + 2 \) and \( y = -x + 6 \), we can set the two equations equal to each other because at the intersection point, the y-values will be the same.

1. Set the equations equal: \[ x + 2 = -x + 6 \]

2. Solve for \( x \): \[ x + x = 6 - 2 \] \[ 2x = 4 \] \[ x = 2 \]

3. Substitute \( x \) back into one of the original equations to find \( y \). We'll use \( y = x + 2 \): \[ y = 2 + 2 = 4 \]

Thus, the intersection point is \((2, 4)\).

In the required format, you can write your answer as: \[ (2, 4) \]