2x+10y=92, -6x-2y=-24

2x+10y=92

-6x-2y=-24

multipy the first equation by 3

then add the equations.
6x-6x+30y-2y=276-24
28y=254
y= 254/28 = 127/14
then put that into either equation and solve for x

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

Let's start with the elimination method. The goal of the elimination method is to eliminate one variable by adding or subtracting the equations. To do this, we want to manipulate one or both equations so that when we add them together, one variable cancels out.

We have the following system of equations:
1) 2x + 10y = 92
2) -6x - 2y = -24

To eliminate the y variable, we need the coefficients of y in both equations to be additive inverses of each other, which means they add up to zero. In this case, we can multiply equation 1 by 2 and equation 2 by 10 to make the coefficients of y match:

Multiplying equation 1 by 2, we get:
3) 4x + 20y = 184

Multiplying equation 2 by 10, we get:
4) -60x - 20y = -240

Now, if we add equation 3 and equation 4 together, the y terms cancel out:
4x + 20y + (-60x) + (-20y) = 184 + (-240)
-56x = -56

Now, we can solve for x by dividing both sides of the equation by -56:
x = -56 / -56 = 1

Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use equation 1:
2(1) + 10y = 92
2 + 10y = 92
10y = 92 - 2
10y = 90
y = 90 / 10 = 9

So, the solution to the system of equations is x = 1 and y = 9.