Question

Use the image to answer the question/
y = 4x - 3
y = -x + 7
Estimate the intersection point of the graphs of the following linear equations in two variables.
y = -x + 7
y = 4x - 3
(__)

Answer 1

To find the intersection point of the equations \( y = 4x - 3 \) and \( y = -x + 7 \), we can set the two equations equal to each other since at the intersection the \( y \) values will be the same:

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

Now, solve for \( x \):

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

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

This simplifies to:

\[
5x - 3 = 7
\]

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

\[
5x = 10
\]

3. Divide by \( 5 \):

\[
x = 2
\]

Now, substitute \( x = 2 \) back into one of the original equations to find \( y \). Using \( y = 4x - 3 \):

\[
y = 4(2) - 3 = 8 - 3 = 5
\]

Thus, the intersection point is \( (2, 5) \).

In the format you provided, it would be represented as:

(2, 5)