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

1 answer

To solve this system of equations using the elimination method, we can multiply the first equation by 5 and the second equation by 3 to make the coefficients of x in both equations the same:

5 * (3x - 4y) = 5 * 40
3 * (5x - 5y) = 3 * 55

Which simplifies to:

15x - 20y = 200
15x - 15y = 165

Now, we can subtract the second equation from the first equation to eliminate x:

(15x - 20y) - (15x - 15y) = 200 - 165

This simplifies to:

-20y + 15y = 35

Combining like terms:

-5y = 35

Dividing both sides by -5:

y = -7

Now, we substitute this value back into one of the original equations to solve for x. Let's use the first equation:

3x - 4(-7) = 40
3x + 28 = 40

Subtracting 28 from both sides:

3x = 12

Dividing both sides by 3:

x = 4

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