Question

3x+3y=6
9x−5y=−24

Answer 1

To solve the system of equations given by

1. \(3x + 3y = 6\)
2. \(9x - 5y = -24\)

we can use the substitution or elimination method. Let's simplify the first equation:

1. Dividing the entire first equation by 3 gives:
\[
x + y = 2
\]
Hence, we can express \(y\) in terms of \(x\):
\[
y = 2 - x
\]

Now we can substitute this expression for \(y\) into the second equation:

2. Substitute \(y = 2 - x\) into \(9x - 5y = -24\):
\[
9x - 5(2 - x) = -24
\]
Distributing \(-5\) gives:
\[
9x - 10 + 5x = -24
\]
Combining like terms results in:
\[
14x - 10 = -24
\]
Adding 10 to both sides:
\[
14x = -14
\]
Dividing both sides by 14 gives:
\[
x = -1
\]

Now that we have \(x\), we can find \(y\) using \(y = 2 - x\):
\[
y = 2 - (-1) = 2 + 1 = 3
\]

So the solution to the system of equations is:
\[
(x, y) = (-1, 3)
\]

To ensure our solution is correct, let's plug \(x\) and \(y\) back into the original equations:

For the first equation:
\[
3(-1) + 3(3) = -3 + 9 = 6 \quad \text{(correct)}
\]

For the second equation:
\[
9(-1) - 5(3) = -9 - 15 = -24 \quad \text{(correct)}
\]

Thus, the solution to the system of equations is:
\[
\boxed{(-1, 3)}
\]