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Solve the system of equations by the addition method.
-x+3y=-4
5x-15y=20

User Chyyran
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1 Answer

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Answer:

To solve the system of equations by the addition method, we need to add the two equations in such a way that one of the variables is eliminated.

Multiplying the first equation by 5, we get:

-5x + 15y = -20

Adding this equation to the second equation, we get:

-5x + 15y = -20

5x - 15y = 20

0x + 0y = 0

This equation tells us that 0 = 0, which is always true. This means that the system of equations has infinitely many solutions, since any value of y will satisfy the equations, and we can then use one of the equations to find the corresponding value of x.

To find a particular solution, we can choose any value of y, say y = 1. Then from the first equation, we have:

-x + 3y = -4

-x + 3(1) = -4

-x = -7

x = 7

Therefore, a particular solution to the system of equations is x = 7 and y = 1. However, there are infinitely many other solutions, since any value of y will satisfy the equations.

User Dgorti
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