Question

Solve the system of equations. −4x+6y=38 x−5y=−20 (1 point)

(35, −3) left parenthesis 35 comma negative 3 right parenthesis

(−5, 3) left parenthesis negative 5 comma 3 right parenthesis

(5, 3) left parenthesis 5 comma 3 right parenthesis

(−35, −3

Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Let's use the substitution method.

From the second equation, solve for \(x\):

\[
x = 5y - 20
\]

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

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

Distributing gives:

\[
-20y + 80 + 6y = 38
\]

Combining like terms:

\[
-14y + 80 = 38
\]

Subtract 80 from both sides:

\[
-14y = 38 - 80
\]
\[
-14y = -42
\]

Divide by -14:

\[
y = \frac{-42}{-14} = 3
\]

Now substitute \(y\) back into the equation for \(x\):

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

So, the solution to the system of equations is:

\[
(x, y) = (-5, 3)
\]

Therefore, the answer is \((−5, 3)\).