Question

The equation below shows when the two lines in the system of equations are equal. Solve for the value of x to find what x equals when the two lines intersect. You can choose to show your work below, or solve on paper and enter your answer on Zearn.
y=2x+3
y=x−7
2x+3
=
x−7

x
=

Answer 1

To find the value of \( x \) where the two lines \( y = 2x + 3 \) and \( y = x - 7 \) intersect, we can set the equations equal to each other since both equations represent \( y \).

So we set:

\[
2x + 3 = x - 7
\]

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

1. Subtract \( x \) from both sides:

\[
2x - x + 3 = -7
\]

This simplifies to:

\[
x + 3 = -7
\]

2. Next, subtract \( 3 \) from both sides:

\[
x = -7 - 3
\]

This simplifies to:

\[
x = -10
\]

So the value of \( x \) at which the two lines intersect is:

\[
\boxed{-10}
\]