Question

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

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:-

$- 7y = 5$

$→y = - \frac{5}{7}$

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:-

$x = - 2( \frac{ - 5}{7}) + 4$

Step 5: Then simplify :-

$y = \frac{38}{7}$

Therefore, the final answer is :-

$x = \frac{38}{7}$

and

$y = \frac{5}{7}$

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Answered by Benjemin360 ☺️