Answer
x = 1
y = -5
Hence, the system of equations only has one solution.
Writing this solution as an ordered pair would require us to put it in the form (x, y). So, the ordered pair solution is
(1, -5)
Step-by-step explanation
We are asked to solve the system of equations and determine how many solutions it has
4x + 5y = -21
6x + 8y = -34
To do this, we try to make the coefficients of x the same; so, we multiply the first equation by 6 and the second equation by 4
(4x + 5y = -21) × 6
(6x + 8y = -34) × 4
24x + 30y = -126
24x + 32y = -136
We can then subtract the first equation from the second equation
24x - 24x + 32y - 30y = -136 - (-126)
0 + 2y = -136 + 126
2y = -10
Divide both sides by 2
(2y/2) = (-10/2)
y = -5
We can then solve for x
4x + 5y = -21
4x + 5(-5) = -21
4x - 25 = -21
4x = -21 + 25
4x = 4
Divide both sides by 4
(4x/4) = (4/4)
x = 1
Hope this Helps!!!