Solve the systems of equations by elimination
3x-5y = 29
2x + 3y = -6
To solve the system of equations by elimination, we need to eliminate one of the variables by manipulating the equations.
Let's multiply the first equation by 2 and the second equation by 3 to make the coefficients of x the same:
(2)(3x - 5y) = 2(29)
(3)(2x + 3y) = 3(-6)
This simplifies to:
6x - 10y = 58
6x + 9y = -18
Now, we can subtract the second equation from the first equation to eliminate x:
(6x - 10y) - (6x + 9y) = 58 - (-18)
6x - 10y - 6x - 9y = 58 + 18
-19y = 76
y = 76 / -19
y = -4
Substitute the value of y into one of the original equations to solve for x. Let's use the first equation:
3x - 5(-4) = 29
3x + 20 = 29
3x = 29 - 20
3x = 9
x = 9 / 3
x = 3
Therefore, the solution to the system of equations is x = 3 and y = -4.