Question

Solve the system of equations.
3x−4y=40
5x−5y=55

Answer 1

To solve this system of equations, we can use the method of substitution or elimination.

In this case, let's use substitution.

From the first equation, we can solve for x in terms of y:
3x - 4y = 40
3x = 4y + 40
x = (4y + 40)/3

Now, substitute this expression for x into the second equation:
5x - 5y = 55
5((4y + 40)/3) - 5y = 55
(20y + 200)/3 - 5y = 55
(20y + 200) - 15y = 165
20y - 15y + 200 = 165
5y + 200 = 165
5y = 165 - 200
5y = -35
y = -35/5
y = -7

Now, substitute this value for y back into one of the original equations:
3x - 4(-7) = 40
3x + 28 = 40
3x = 40 - 28
3x = 12
x = 12/3
x = 4

So the solution to the system of equations is x = 4 and y = -7.