Question

find the solution of the system of equations
4x + 10y=-24
-2x + y= -24

Answer 1

To solve the system of equations:

1. \( 4x + 10y = -24 \) (Equation 1)
2. \( -2x + y = -24 \) (Equation 2)

We can use substitution or elimination. Here, we'll use the substitution method.

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

\[
y = -24 + 2x
\]

Now, substitute \( y \) in Equation 1:

\[
4x + 10(-24 + 2x) = -24
\]

Distributing the \( 10 \):

\[
4x - 240 + 20x = -24
\]

Combine like terms:

\[
(4x + 20x) - 240 = -24
\]
\[
24x - 240 = -24
\]

Now, add 240 to both sides:

\[
24x = 216
\]

Divide by 24:

\[
x = 9
\]

Now, substitute \( x = 9 \) back into the equation for \( y \):

\[
y = -24 + 2(9)
\]
\[
y = -24 + 18
\]
\[
y = -6
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (9, -6)
\]