Question

Solve the system by Substitution.

-4x + y = 0
2x - 3y = -10

(1 point)
Responses

(1,4)
(1,4)

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

(3,2)

Answer 1

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

1) \(-4x + y = 0\)

2) \(2x - 3y = -10\)

First, we can solve the first equation for \(y\):

From equation (1):
\[
y = 4x
\]

Next, we substitute \(y = 4x\) into the second equation (2):

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

Now simplify this:
\[
2x - 12x = -10
\]
\[
-10x = -10
\]

Now, divide both sides by -10:
\[
x = 1
\]

Now that we have \(x\), we substitute it back into the equation for \(y\):
\[
y = 4(1) = 4
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (1, 4)
\]

So the answer is:
\[
(1, 4)
\]