Question

2x+3y=30
-12x+8y=-24
Answer by elimanation

Answer 1

To solve the system of equations using the elimination method, we start with the two equations:

1. \( 2x + 3y = 30 \) (Equation 1)
2. \( -12x + 8y = -24 \) (Equation 2)

We'll manipulate these equations to eliminate one of the variables. Let's eliminate \(x\).

First, we can multiply Equation 1 by 6 to make the coefficient of \(x\) the same in both equations. This gives us:

\[
6(2x + 3y) = 6(30)
\]
\[
12x + 18y = 180 \quad (Equation 3)
\]

Now we have:

1. \( 12x + 18y = 180 \) (Equation 3)
2. \( -12x + 8y = -24 \) (Equation 2)

Next, we add Equation 3 and Equation 2 together:

\[
(12x + 18y) + (-12x + 8y) = 180 + (-24)
\]

This simplifies to:

\[
0x + 26y = 156
\]

So we have:

\[
26y = 156
\]
Dividing both sides by 26 gives:

\[
y = 6
\]

Now that we have \(y\), we can substitute it back into one of the original equations to solve for \(x\). We'll use Equation 1:

\[
2x + 3(6) = 30
\]
\[
2x + 18 = 30
\]
Subtracting 18 from both sides gives:

\[
2x = 12
\]
Dividing both sides by 2 gives:

\[
x = 6
\]

So the solution to the system of equations is:

\[
x = 6, \quad y = 6
\]

Thus, the solution is \( (x, y) = (6, 6) \).