Solve the system of two linear equations.
-3x-4y=-23
3x-5y=5
(5,-2)
(-5, 2)
(-5,-2)
(5, 2)
Let's solve the given system of two linear equations step by step:
Equation 1: -3x - 4y = -23
Equation 2: 3x - 5y = 5
We can use either substitution or elimination to solve for x and y. I will use the elimination method by adding both equations to eliminate the x variable:
-3x - 4y = -23
+
3x - 5y = 5
-------------------
-9y = -18
Now, divide both sides by -9:
y = -18 / -9
y = 2
Now that we have the value of y, we can substitute it back into either equation to solve for x. Let's use Equation 2:
3x - 5y = 5
3x - 5(2) = 5
3x - 10 = 5
3x = 5 + 10
3x = 15
x = 15 / 3
x = 5
So, the solution to the system of equations is (x, y) = (5, 2). This corresponds to the option (5, 2).