Solve the system using elimination.
5 x minus 9 y equals negative 43.
3 x plus 8 y equals 68.
To solve the system using elimination, we need to manipulate one or both of the equations so that when we add or subtract them, one of the variables cancels out.
Let's start by multiplying the first equation by 3 and the second equation by 5 to make the coefficients of x the same:
(3)(5x - 9y) = (3)(-43)
(5)(3x + 8y) = (5)(68)
Which simplifies to:
15x - 27y = -129
15x + 40y = 340
Now we can eliminate the x variable by subtracting the second equation from the first equation:
(15x - 27y) - (15x + 40y) = -129 - 340
15x - 27y - 15x - 40y = -469
-67y = -469
y = -469 / -67
y = 7
Now substitute the value of y back into either equation to solve for x. Let's use the first equation:
5x - 9(7) = -43
5x - 63 = -43
5x = -43 + 63
5x = 20
x = 20 / 5
x = 4
So the solution to the system of equations is x = 4, y = 7.