Question

Solve the sytsem of two linear equations. -3x - 4y = -23
3x - 5y = 5

Answer 1

To solve the system of equations:

1. \(-3x - 4y = -23\) (Equation 1)
2. \(3x - 5y = 5\) (Equation 2)

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

First, let's eliminate \(x\) by adding the two equations together. We'll multiply Equation 2 by 1 (to make it easier) and then add them:

\[
-3x - 4y = -23 \quad \text{(1)}
\]
\[
3x - 5y = 5 \quad \text{(2)}
\]

Add Equation 1 and Equation 2:
\[
(-3x + 3x) + (-4y - 5y) = -23 + 5
\]
This simplifies to:
\[
0 - 9y = -18
\]
So:
\[
-9y = -18
\]
Dividing both sides by \(-9\):
\[
y = 2
\]

Now that we have \(y\), we can find \(x\) by substituting \(y = 2\) back into one of the original equations. Using Equation 2:

\[
3x - 5(2) = 5
\]
This simplifies to:
\[
3x - 10 = 5
\]
Adding 10 to both sides:
\[
3x = 15
\]
Dividing both sides by 3:
\[
x = 5
\]

So the solution to the system of equations is:
\[
x = 5, \quad y = 2
\]

Therefore, the solution is \((x, y) = (5, 2)\).