X-2y=-11 7x-10y=7

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

First, let's multiply the first equation by 7 and the second equation by 2 to make the coefficients of x in both equations the same:

7(x-2y) = 7(-11) 2(7x-10y) = 2(7)

Simplifying these:

7x - 14y = -77 14x - 20y = 14

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

(7x - 14y) - (14x - 20y) = -77 - 14

Simplifying further:

7x - 14y - 14x + 20y = -91 -7x + 6y = -91

Now, let's solve for y by isolating it:

-7x + 6y = -91 6y = 7x - 91 y = (7x - 91) / 6

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

x - 2(7x - 91) / 6 = -11 6x - 2(7x - 91) = -66 6x - 14x + 182 = -66 -8x = -248 x = -248 / -8 x = 31

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

31 - 2y = -11 -2y = -11 - 31 -2y = -42 y = -42 / -2 y = 21

So, the solution to the system of equations is x = 31 and y = 21.