Question

solve the system of quations. -4x + 6y = 38
x - 5y = -20

Answer 1

To solve the system of equations:

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

We can use the substitution or elimination method. Here, I will use the substitution method.

First, we can express \(x\) in terms of \(y\) from Equation 2:

\[
x = 5y - 20
\]

Next, we can substitute this expression for \(x\) into Equation 1:

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

Distributing \(-4\):

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

Combine like terms:

\[
-14y + 80 = 38
\]

Now, isolate \(y\):

\[
-14y = 38 - 80
\]
\[
-14y = -42
\]
\[
y = \frac{-42}{-14} = 3
\]

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

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

The solution to the system of equations is:

\[
x = -5, \quad y = 3
\]

So, the solution is \((-5, 3)\).