Solve each system algebraically:

1. \(3x + 6y = -6\)

2. \(5x - 2y = 14\)

If you multiply the second equation by 3, it becomes:
15x - 6y = 42
Then add the two equations together:
3x + 6y = -6 15x - 6y = 42 +
18x = 36 x = 2
substitute x back into the first equation:
3(2)+6y = -6 6 + 6y = -6 6y = -12 y = -2
So x=2,y=-2

Answered by ollieboyne | 2024-06-10

{ 5 x − 2 y = 14 ∣ ∗ 3 3 x + 6 y = − 6 ​ { 15 x − 6 y = 42 3 x + 6 y = − 6 ​ \+ − − − − − A dd i t i o n m e t h o d 18 x = 36 ∣ d i v i d e b y 18 x = 2 2 y = 5 x − 14 y = 2 5 x − 14 ​ = 2 5 ∗ 2 − 14 ​ = 2 10 − 14 ​ = − 2 S o l u t i o n { x = 2 y = − 2 ​

Answered by luana | 2024-06-10

The solution to the system of equations 3 x + 6 y = − 6 and 5 x − 2 y = 14 is x = 2 and y = − 2 . This can be found using the elimination method. By manipulating the equations and substituting back, we arrive at the final solution.
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Answered by ollieboyne | 2024-12-26