Question

Solve the system of equations using elimination: 9x+y=−9 and −8x−2y=54.

Answer 1

The solution to the system of equations 9x + y = -9 and -8x - 2y = 54 using elimination is x = 3.6 and y = -41.4, found by first multiplying the first equation by 2 to eliminate y and then solving for x.

Step-by-step explanation:

To solve the system of equations 9x + y = -9 and -8x - 2y = 54 using elimination, we want to eliminate one of the variables so that we can solve for the other.

1. Multiply the first equation by 2 to get the coefficients of y to be opposites:
2. 2(9x + y) = 2(-9) → 18x + 2y = -18
3. Now add this new equation to the second equation:
4. (18x + 2y) + (-8x - 2y) = -18 + 54 → 10x = 36
5. Divide both sides by 10 to solve for x:
6. 10x/10 = 36/10 → x = 3.6
7. Substitute x = 3.6 back into one of the original equations to solve for y:
8. 9(3.6) + y = -9 → 32.4 + y = -9
9. Subtract 32.4 from both sides:
10. y = -9 - 32.4 → y = -41.4

The solution to the system of equations is x = 3.6 and y = -41.4.