Question

solve the system of equations

-4x + 6y = 38
x - 5y = -20

(-5, 3)
(35, -3)
(-35, -3)
(5, 3)

Answer 1

To solve the system of equations

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

we can use substitution or elimination. Here, I'll use the substitution method for clarity.

From the second equation, we can express \(x\) in terms of \(y\):

\[
x = 5y - 20
\]

Now, we can substitute this expression for \(x\) into the first equation:

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

Distributing the \(-4\):

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

Combining like terms:

\[
-14y + 80 = 38
\]

Next, isolate \(y\) by moving 80 to the other side:

\[
-14y = 38 - 80
\]

\[
-14y = -42
\]

Dividing both sides by \(-14\):

\[
y = 3
\]

Now that we have \(y\), substitute it back into the equation for \(x\):

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

\[
x = 15 - 20
\]

\[
x = -5
\]

The solution to the system of equations is:

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

From the options provided, the correct answer is \((-5, 3)\).