Question

Use the image to answer the question.
3x - 2y = -4
x - 5y = 3
Review the graphs of a system of two linear equations in two variables: x - 5y = 7 and 3x - 2y = -4. Find the solution to both equations.
The intersection point is (__).

Answer 1

To find the solution to the system of linear equations given by:

1. \( 3x - 2y = -4 \)
2. \( x - 5y = 3 \)

we can solve the equations using substitution or elimination. In this case, let's use substitution.

First, solve the second equation for \( x \):

\[
x = 5y + 3
\]

Now, substitute this expression for \( x \) into the first equation:

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

Expand and simplify:

\[
15y + 9 - 2y = -4
\]

Combine like terms:

\[
13y + 9 = -4
\]

Subtract 9 from both sides:

\[
13y = -4 - 9
\]
\[
13y = -13
\]

Now, divide by 13:

\[
y = -1
\]

Next, substitute \( y = -1 \) back into the equation \( x = 5y + 3 \):

\[
x = 5(-1) + 3
\]
\[
x = -5 + 3
\]
\[
x = -2
\]

Thus, the solution to the system is \( (x, y) = (-2, -1) \).

So, the intersection point is **(-2, -1)**.