What is the solution of the system? 5x + 7y = 32 8x + 6y = 46
To solve the system of equations, we can use either substitution or elimination method. We'll use the elimination method:
Multiply the first equation by 8 and the second equation by 5 to get:
40x + 56y = 256
40x + 30y = 230
Now, subtract the second equation from the first equation:
(40x + 56y) - (40x + 30y) = 256 - 230
40x - 40x + 56y - 30y = 26
26y = 26
Divide both sides by 26 to solve for y:
y = 26/26
y = 1
Substitute the value of y into one of the original equations, let's use the first equation:
5x + 7(1) = 32
5x + 7 = 32
5x = 32 - 7
5x = 25
Divide both sides by 5 to solve for x:
x = 25/5
x = 5
Therefore, the solution to the system of equations is x = 5 and y = 1.