Solve the system of two linear equations. −3x−4y=−23, 3x−5y=5

Answer 1

To solve this system of equations, we can use the method of substitution or elimination.

Let's use the elimination method to solve this system of equations.

Start by multiplying the second equation by 3 to make the coefficients of x in both equations the same.

Original equations:
-3x - 4y = -23
3x - 5y = 5

Multiply the second equation by 3:
9x - 15y = 15

Now, add the two equations together to eliminate x:
(-3x - 4y) + (9x - 15y) = -23 + 15
6x - 19y = -8

Next, solve for y by isolating it in the equation:
-19y = -8 - 6x
-19y = -8 - 6x
y = (8 + 6x) / 19

Now, substitute this value of y back into one of the original equations to solve for x. Let's use the first equation:
-3x - 4((8 + 6x) / 19) = -23
-3x - (32 + 24x) / 19 = -23
-57x - 32 - 24x = -437
-57x - 24x = -437 + 32
-81x = -405
x = -405 / -81
x = 5

Now that we have found the value of x, we can substitute it back into either of the original equations to solve for y. Let's use the second equation:
3(5) - 5y = 5
15 - 5y = 5
-5y = -10
y = -10 / -5
y = 2

Therefore, the solution to the system of equations is x = 5, y = 2.