22x + 17y = 15

15x - 4y = 57

What is the solution for the system of equations above?

1 answer

To solve this system of equations, we can use the method of elimination. First, let's eliminate one of the variables. To do this, we'll multiply the first equation by 4 and the second equation by 17:

(4)(22x + 17y) = (4)(15)
(17)(15x - 4y) = (17)(57)

88x + 68y = 60
255x - 68y = 969

Next, we'll add these two equations together:

(88x + 68y) + (255x - 68y) = 60 + 969
343x = 1029

Finally, we divide both sides of the equation by 343 to solve for x:

x = 1029/343
x = 3

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

22x + 17y = 15
22(3) + 17y = 15
66 + 17y = 15
17y = 15 - 66
17y = -51
y = -51/17
y = -3

Therefore, the solution for the system of equations is x = 3 and y = -3.