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What makes this approach a valid method in general for solving a system of equations?

Updated January 19, 2025

Derrick adds equations A and B to solve this system of equations. What makes this approach a valid method in general for solving a system of equations?

As long as addition is used on both sides or subtraction is used on both sides, a true equation will remain true.

Because the y-terms cancel: (5x + 4y) + (3x – 4y) = 5x + 3x + 4y – 4y = 8x

Adding a quantity like 5x + 4y to one side of an equation and another quantity like 24 to the other side maintains the equality if the two quantities are equal.

The method will give the correct solution, x = 5 and y = -1/4. 5(5) + 4(-1/4) = 24; 3(5) – 4(-1/4) = 16

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Quizzma TeamJanuary 19, 2025

To solve a system of equations by adding the equations together, the fundamental principle is that as long as the same operation is applied to both sides of the equation, the true nature of the equation is preserved.

So, the correct response is:

As long as addition is used on both sides or subtraction is used on both sides, a true equation will remain true.

This principle allows for manipulating the equations to eliminate variables and solve for the others, which is essential in finding the correct solutions. Keep practicing these techniques, and you’ll become even proficient at solving systems of equations!