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.

Question

y=2x+3
y=x−7
2x+3
=
x−7
x
=

Answer 1

To find the value of \( x \) where the two lines intersect, we can set the equations equal to each other since both are equal to \( y \):

1. \( y = 2x + 3 \)
2. \( y = x - 7 \)

Setting the two equations equal to each other gives:

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

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:

\[ x = -10 \]

Thus, the value of \( x \) when the two lines intersect is

\[ \boxed{-10} \]