Question

Solve the system of equations.
-4x + 6у = 38
x - 5y = -20 (1 point)
(-35, - 3)
(5, 3)
(35, - 3)
(-5,3）

Answer 1

To solve the system of equations, we start by rewriting the equations:

1. \(-4x + 6y = 38\)
2. \(x - 5y = -20\)

Now, we can solve one of the equations for one variable and substitute it into the other. Let's solve the second equation for \(x\):

From \(x - 5y = -20\):
\[
x = 5y - 20
\]

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

\[
-4(5y - 20) + 6y = 38
\]

Distributing \( -4 \):
\[
-20y + 80 + 6y = 38
\]

Combine like terms:
\[
-14y + 80 = 38
\]

Subtract 80 from both sides:
\[
-14y = 38 - 80
\]
\[
-14y = -42
\]

Now, divide by -14:
\[
y = \frac{-42}{-14} = 3
\]

Now that we have \(y\), we can find \(x\) using the equation \(x = 5y - 20\):

\[
x = 5(3) - 20
\]
\[
x = 15 - 20
\]
\[
x = -5
\]

So, the solution to the system of equations is \( (x, y) = (-5, 3) \).

Thus, the correct answer is:
\[
\boxed{(-5, 3)}
\]