To find the solution to the system of equations:
1) 4x + 5y = 7
2) 3x - 2y = -12
You can use methods like substitution or elimination. Let's use the elimination method:
First, let's multiply the second equation by 2 to make the coefficients of y in both equations equal:
2(3x - 2y) = 2(-12)
6x - 4y = -24
Now, we have the system of equations:
1) 4x + 5y = 7
2) 6x - 4y = -24
Next, we can multiply the first equation by 3 and the second equation by 4 to make the coefficients of x in both equations equal:
3(4x + 5y) = 3(7)
12x + 15y = 21
4(6x - 4y) = 4(-24)
24x - 16y = -96
Now, we have the system of equations:
1) 12x + 15y = 21
2) 24x - 16y = -96
Now, let's multiply the first equation by 2:
2(12x + 15y) = 2(21)
24x + 30y = 42
Now we have:
1) 24x + 30y = 42
2) 24x - 16y = -96
We can subtract the first equation from the second equation to eliminate x:
(24x - 16y) - (24x + 30y) = -96 - 42
-46y = -138
y = 3
Now that we have the value of y, we can substitute it back into the original second equation:
3x - 2(3) = -12
3x - 6 = -12
3x = -6
x = -2
So, the solution to the system of equations is x = -2 and y = 3.