Use the image to answer the question.

Question

An illustration of a coordinate plane with four quadrants shows 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 7. The equation of the dotted line is y equals 4 x minus 3. The lines intersect at left parenthesis 2 comma 5 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+7


y=4x−3


(1 point)
(
,
)
Remaining Attempts : 3

Answer 1

To find the intersection point of the two lines given by the equations \( y = -x + 7 \) and \( y = 4x - 3 \), we need to set the two equations equal to each other because at the intersection point, the y-values will be the same.

Setting the equations equal: \[ -x + 7 = 4x - 3 \]

Now, we can solve for \( x \):

1. Add \( x \) to both sides: \[ 7 = 5x - 3 \]
2. Add 3 to both sides: \[ 10 = 5x \]
3. Divide by 5: \[ x = 2 \]

Now that we have \( x = 2 \), we can substitute this value back into either of the original equations to find the corresponding \( y \)-value. We'll use the first equation \( y = -x + 7 \): \[ y = -2 + 7 = 5 \]

So the intersection point of the graphs of the equations is: \[ (2, 5) \]

The answer is \( (2, 5) \).