Question

Use the linear combination method to solve the system of equations. *Explain each step of your solution.

2x - 3y = 13
x + 2y = 4

Answer 1

Step 1: We have the next system of equations -

`2x - 3y = 13`

`x + 2y = 4`

Step 2: Now, we will multiply by -2 the second equation:-

`- 2(x + 2y) = 4`

`→ - 2x - 4y = - 8`

Step 3: Then we add it :-

`2x - 3y = 13`

`( + ) \: - 2x - 4y = - 8`

Step 4: After finding the sum, we simplify:-

`- 7y = 5`

`→y = - (5)/(7)`

Then, substitute the above y value to find x's value in any equation of Step 1. Now, I used to second equation in Step 1:-

`x = - 2( ( - 5)/(7)) + 4`

Step 5: Then simplify :-

`y = (38)/(7)`

Therefore, the final answer is :-

`x = (38)/(7)`

and

`y = (5)/(7)`

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Answered by Benjemin360 ☺️