Question

Given the following systems, determine the solution for x and y, using the elimination method

1)
x + 4y = 12
2x −y = 6

2)
−x + 3y = 4
3x −4y = −2

Answer 1

Explanation:

elimination method :

multiply one or both equations by factors and then add them or subtract one from the other, so that one variable is eliminated, and we solve the rest for the remaining variable.

1)

e.g. multiply the second equation by 4 and then add both equations :

x + 4y = 12

8x - 4y = 24

-------------------

9x 0 = 36

9x = 36

x = 4

x + 4y = 12

4 + 4y = 12

4y = 8

y = 2

2)

multiply the first equation by 3 and then add both equations :

-3x + 9y = 12

3x - 4y = -2

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0 5y = 10

y = 2

-x + 3y = 4

-x + 3×2 = 4

-x + 6 = 4

-x = -2

x = 2