Question

Which ordered pair represents the solution to the system of equations? {−5x+7y=−196x−2y=10

Answer 1

Answer:
x = 1
y = -2

Explanation:
First, solve for x by subtracting 7y from both sides of the first equation and then divide both sides by -5.

-5x + 7y = -19
-5x + 7y - 7y = -19 - 7y
-5x = -19 - 7y
-5x/ -5 = -19 - 7y/ -5
x = -19 - 7y/ -5

Next, substitute the value of x into the second equation and solve.

6 - (-19 - 7y)/ 5 - 2y = 10
- 6(-19 - 7y)/ 5 - 2y = 10

Then, solve for y

- 6(-19 - 7y)/ 5 - 2y = 10
-6(-19 - 7y) - 10y = 50
114 + 42y - 10y = 50
144 + 32y = 50
32y = 50 - 144
32y = -64
32y/ 32 = -64/ 32
y = -2

Finally, substitute the value of y into the x value we found earlier and solve

x = - 19 - 7y/ 5
x = - 19 - 7 • -2/ 5
x = 1