Question

Solve the system by Substitution.
y = 2x + 5
3x - 4y = 10(1 point)
Responses

(5,2)
(5,2)

(-6, -7)
(-6, -7)

(-2,1)

Answer 1

To solve the system of equations using substitution, we start with the two equations given:

1. \( y = 2x + 5 \)
2. \( 3x - 4y = 10 \)

Since we already have \( y \) expressed in terms of \( x \) from the first equation, we can substitute this expression for \( y \) into the second equation.

Substituting \( y = 2x + 5 \) into the second equation:

\[
3x - 4(2x + 5) = 10
\]

Now distribute the -4:

\[
3x - 8x - 20 = 10
\]

Combine like terms:

\[
-5x - 20 = 10
\]

Now, isolate \( x \):

\[
-5x = 10 + 20
\]
\[
-5x = 30
\]
\[
x = -6
\]

Now that we have \( x \), we substitute it back into the first equation to solve for \( y \):

\[
y = 2(-6) + 5
\]
\[
y = -12 + 5
\]
\[
y = -7
\]

So the solution to the system of equations is:

\[
(x, y) = (-6, -7)
\]

Thus, the answer is:

**(-6, -7)**