twice a number plus twice a second number is 310. The difference between the numbers is 55

Accepted Solution

Answer:x = 105y = 50Step-by-step explanation:To solve this, try writing it out as an equation/expression first.When you do, you should get something like this:2x + 2y = 310x - y = 55This is a system of equations. To solve this, we're going to multiply the second equation [x - y = 55] by 2.2(x - y = 55) = 2x - 2y = 110Now, subtract your new equation from the first one [2x + 2y = 310]2x + 2y = 310-2x + 2y = -110//If you're wondering why I changed the signs of the new equation, I multiplied our new equation [2x - 2y = 110] by -1 since we're subtracting//When you're done subtracting, the "2x" and "-2x" cancel out, so you're left with:4y = 200Now, simply solve for "y" by dividing both sides by 4.4y = 200y = 50Now that we know y's value, substitute it into one of our original equations to solve for x.//I'm gonna plug y into the second equation [x - y = 55] just because it's easier, but you can plug it into the first one as well and get the same answer//When we plug it in, we get:x - (50) = 55To solve for "x," we must get rid of "-50." To do this, add 50 to both sides.x - 50 = 55x = 105So, x = 105 and y = 50