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A math student has a plan to solve the following system by the elimination method. To eliminate the x-terms, he wants to multiply the top equation by 7 . What should he multiply the second equation by so that when he adds the equations, the x-terms are eliminated?

A math student has a plan to solve the following system by the elimination method-example-1
User Makis
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1 Answer

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Answer

To eliminate x, we will multiply the second equatio by -3.

x = 7

y = 5

Step-by-step explanation

To solve this, we first write the two equations

-3x - 7y = -56

-7x + 10y = 1

So, to solve this, we need to make sure the factors of x are the same numbers and of opposite signs

So, if we multiply the first equation by 7, we will need to multiply the second equation by -3 to obtain 21x and -21x for the two of them.

(-3x - 7y = -56) × 7

(-7x + 10y = 1) × -3

-21x - 49y = -392

21x - 30y = -3

We will then add the two equations and then the solution for the equation is obtained by solving for y first.

-21x + 21x - 49y - 30y = -392 - 3

0 - 79y = -395

-79y = -395

Divide both sides by -79

(-79y/-79) = (-395/-79)

y = 5

We can then solve for x using any of the two equations

-7x + 10y = 1

-7x + 10(5) = 1

-7x + 50 = 1

-7x = 1 - 50

-7x = -49

Divide both sides by -7

(-7x/-7) = (-49/-7)

x = 7

Hope this Helps!!!

User Wulymammoth
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