Solve the system of two linear equations

Negative 3X minus 4Y equals -23
2X minus 5Y equals five

1 answer

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

Given equations:
-3X - 4Y = -23 (1)
2X - 5Y = 5 (2)

To eliminate X, we need to multiply equation (1) by 2 and equation (2) by 3:
-6X - 8Y = -46 (3)
6X - 15Y = 15 (4)

Now, add equations (3) and (4) together:
-23Y = -31
Y = -31 / -23
Y = 31 / 23

Now substitute the value of Y back into equation (1):
-3X - 4(31/23) = -23
-3X - 124 / 23 = -23
-3X = -23 + 124 / 23
-3X = -23(23) / 23 + 124 / 23
-3X = -529 / 23 + 124 / 23
-3X = -405 / 23
X = -405 / -3 / 23
X = 135 / 23

Therefore, the solution to the system of equations is:
X = 135/23
Y = 31/23