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.

Question

Estimate the intersection point of the graphs of the following linear equations in two variables.

y=−x+7


y=4x−3


(1 point)
(
,
)

Answer 1

To find the intersection point of the two lines given by the equations \( y = -x + 7 \) and \( y = 4x - 3 \), we can set the two equations equal to each other:

\[ -x + 7 = 4x - 3 \]

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

1. Add \( x \) to both sides:

\[ 7 = 5x - 3 \]

2. Add \( 3 \) to both sides:

\[ 10 = 5x \]

3. Divide both sides by \( 5 \):

\[ x = 2 \]

Next, we substitute \( x = 2 \) back into one of the original equations to find \( y \). We can use either equation; let's use \( y = -x + 7 \):

\[ y = -2 + 7 = 5 \]

Thus, the intersection point of the two lines is:

\[ (2, 5) \]

So, the estimated intersection point is:

\[ \boxed{(2, 5)} \]