Answer:
The solution to the system of equations is x = -6 and y = -4.
Step-by-step explanation:
To eliminate a variable, we need to find a multiple of one equation that can be added or subtracted to the other equation to eliminate that variable.
In this case, multiplying the first equation by 5 and the second equation by 2 will allow us to eliminate the x variable:
5(3x + 2y) = 5(-26)
2(4x - 5y) = 2(-4)
Simplifying:
15x + 10y = -130
8x - 10y = -8
Now, add the two equations together:
(15x + 10y) + (8x - 10y) = -130 + (-8)
23x = -138
Divide both sides of the equation by 23:
x = -138/23
x = -6
Now, substitute the value of x into either of the original equations to solve for y. Let's use the first equation:
3(-6) + 2y = -26
-18 + 2y = -26
2y = -26 + 18
2y = -8
y = -8/2
y = -4
Therefore, the solution to the system of equations is x = -6 and y = -4.
