Question

what is the solution of the system
5x+7y=32
8x+6y=46

Answer 1

To solve the system of equations, you can use the method of substitution or elimination. Here, we will use the method of elimination.

Multiply the first equation by 8 and the second equation by 5 to make the coefficients of x in both equations equal:

8(5x + 7y) = 8(32)
5(8x + 6y) = 5(46)

This simplifies the system to:
40x + 56y = 256
40x + 30y = 230

Subtract the second equation from the first equation to eliminate the x variable:
(40x + 56y) - (40x + 30y) = 256 - 230
40x + 56y - 40x - 30y = 26
26y = 26
y = 1

Substitute the value of y = 1 into one of the original equations (let's use the first equation) and solve for x:
5x + 7(1) = 32
5x + 7 = 32
5x = 32 - 7
5x = 25
x = 5

Therefore, the solution to the system of equations is x = 5, y = 1.