solve the system of equations,
-x + 6y = 13
4x-10y =-10
To solve this system of equations, we can use the method of substitution or elimination. I will use the method of elimination.
Given equations:
1. -x + 6y = 13
2. 4x - 10y = -10
We will first multiply the first equation by 4 and the second equation by 1 to make the coefficients of x the same but opposite in sign. This will allow us to add the equations together to eliminate x.
1. (-x + 6y)*4 = 13*4
-4x + 24y = 52
2. 4x - 10y = -10
Now, add the two equations together:
-4x + 24y + 4x - 10y = 52 - 10
14y = 42
Divide by 14 on both sides:
y = 42 / 14
y = 3
Now, substitute the value of y back into one of the original equations to solve for x. I will use the first equation:
-x + 6(3) = 13
-x + 18 = 13
-x = 13 - 18
-x = -5
x = 5
Therefore, the solution to the system of equations is:
x = 5, y = 3.