Solve the system of two linear equations.

- 3x - 4y = - 23
3x - 5y = 5 (1 point)

1 answer

To solve the system of two linear equations, we'll use the method of elimination.

First, let's multiply the second equation by -1 to make the coefficients of x in both equations opposites:

-1(3x - 5y) = -1(5)
-3x + 5y = -5

Now we have these two equations:

-3x - 4y = -23
-3x + 5y = -5

Next, we'll add these two equations together to eliminate x:

(-3x - 4y) + (-3x + 5y) = -23 + (-5)
-3x - 3x - 4y + 5y = -23 - 5
-6x + y = -28

Now, we'll isolate y in this equation:

y = -6x - 28

We can substitute this expression for y in one of the original equations. Let's use the first equation:

-3x - 4(-6x - 28) = -23
-3x + 24x + 112 = -23
21x + 112 = -23
21x = -23 - 112
21x = -135
x = -135/21
x = -45/7

Now, substitute this value for x back into the expression for y:

y = -6(-45/7) - 28
y = 270/7 - 196/7
y = 74/7

Therefore, the solution to the system of equations is x = -45/7 and y = 74/7.