Question

Solve the system using Substitution.

−4x+y=0

2x−3y=−10


(1 point)
Responses

(1,4)
(1,4)

(-2,3)
(-2,3)

(0,-5)
(0,-5)

(3,2)

Answer 1

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

1. \( -4x + y = 0 \) (Equation 1)
2. \( 2x - 3y = -10 \) (Equation 2)

First, we can solve Equation 1 for \( y \):

\[
y = 4x
\]

Next, we substitute \( y = 4x \) into Equation 2:

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

This simplifies to:

\[
2x - 12x = -10
\]
\[
-10x = -10
\]
\[
x = 1
\]

Now that we have the value of \( x \), we can find \( y \) by substituting \( x = 1 \) back into our expression for \( y \):

\[
y = 4(1) = 4
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (1, 4)
\]

Therefore, the answer is:

\((1, 4)\)