Solve the system of equations by equations

-x+6y=13
4x-10y=-10

1 answer

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

First, multiply the first equation by 4 and the second equation by -1 to make the coefficients of x the same:

-4x + 24y = 52
-4x + 10y = 10

Now, add these two new equations together:

14y = 62

Divide by 14 to solve for y:

y = 62/14
y = 31/7

Now, substitute this value of y back into one of the original equations to solve for x:

-x + 6(31/7) = 13
-x + 186/7 = 13
-x = 13 - 186/7
-x = 91/7 - 186/7
-x = -95/7
x = 95/7

Therefore, the solution to the system of equations is x = 95/7 and y = 31/7.