22x + 17y = 15
15x - 4y = 57
What is the solution for the system of equations above?
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.