Question

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

Answer 1

To solve the system of equations:

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

We can solve these equations using the substitution or elimination methods. Let's use the substitution method.

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

\[
x = 5y - 20
\]

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

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

Expanding this:

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

Combine like terms:

\[
-14y + 80 = 38
\]

Now, isolate \(y\) by subtracting 80 from both sides:

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

Now, divide by -14:

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

Now that we have \(y\), substitute back to find \(x\) using the expression \(x = 5y - 20\):

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

Thus, the solution to the system of equations is:

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

The solution can be written as the ordered pair \((-5, 3)\).