Question

Solve the system of equations using elimination: minus, 5, x, plus, 8, y, equals, 5−5x+8y=5 and x, minus, 2, y, equals, 1x−2y=1.

Answer 1

To solve the system of equations using elimination, we want to eliminate one variable by manipulating the equations.

First, let's multiply the second equation by 5 to make the coefficients of x in both equations equal.
5(x - 2y) = 5(1)
5x - 10y = 5

Now we have the equations:
-5x + 8y = 5
5x - 10y = 5

Adding these two equations together, we can eliminate the x variable.
(-5x + 8y) + (5x - 10y) = 5 + 5
-2y = 10

Now, dividing both sides of the equation by -2, we can isolate the y variable.
-2y/-2 = 10/-2
y = -5

Substituting this value of y into either of the original equations, we can solve for x.
5 - 5x + 8(-5) = 5
-5x - 40 = 0
-5x = 40
x = -8

Therefore, the solution to the system of equations is x = -8 and y = -5.