To solve this system of equations, we want to add or subtract the equations so that either x or y cancels out.
We can multiply the first equation by -2, so that 5y will become -10y, and then add the equation with the second so -10y and 10y will cancel out.
Multiplying the first equation by -2, we get: -4x - 10y = -30
Add this to the second equation and we get: x = 5
So, we have x = 5. However, we should plug it into both equations to solve for y and make sure both answers check out.
Doing this for the first equation, we have: 2(5) + 5y = 15 10 + 5y = 15 Subtract 10 from both sides to get: 5y = 5 Divide by 5 on both sides to get: y = 1
We will now see if x = 5 and y = 1 works for the second equation. 5x + 10y = 35 5(5) + 10(1) = 35 35 = 35, checks out
