Question

Solve the system by Substitution.
y=2x+5

3x−4y=10
(1 point)
Responses

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

(4,3)
(4,3)

(-2,1)
(-2,1)

(5,2)
(5,2)

Answer 1

To solve the system of equations using substitution, we have the following equations:

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

We can substitute Equation 1 into Equation 2.

Starting with Equation 2:
\[
3x - 4y = 10
\]

Substituting \( y = 2x + 5 \) into Equation 2:
\[
3x - 4(2x + 5) = 10
\]

Now simplify:
\[
3x - 8x - 20 = 10
\]
\[
-5x - 20 = 10
\]

Now, isolate \( x \):
\[
-5x = 10 + 20
\]
\[
-5x = 30
\]
\[
x = -6
\]

Now that we have \( x \), substitute it back into Equation 1 to find \( y \):
\[
y = 2(-6) + 5
\]
\[
y = -12 + 5
\]
\[
y = -7
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (-6, -7)
\]

So the answer is:
\[
\boxed{(-6, -7)}
\]