`4x - 3y = 0` `-10x + 7y = -2` Solve the system using the linear combination method.

Textbook Question

Chapter 3, 3.2 - Problem 9 - McDougal Littell Algebra 2 (1st Edition, Ron Larson).
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taangerine | Student, Grade 12 | (Level 1) Valedictorian

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Before we use the linear combination method, we have to see which one would be easier to cancel out (act as out opposites). For example, -2x and +2x would be an opposite and will cancel out. In this case(since there are no opposites), we would have to make an opposite. You can multiply and create opposites to either the x or the y. I will be doing it to the x to create an opposite.

Multiply 10 to the top equation and rewrite it. Multiply 4 to the 2nd equation and rewrite it.

10(4x-3y=0)         40x-30y=0

4(-10x+7y=-2)    -40x+28y=-8

40x and -40x are our opposites. Arrange the two equations on top of each other and do it like addition.

  40x-30y=0

-40x+28y=-8

________________

         -2y=-8

Solve by dividing.

            y=-8/-2=4

Now that you've found y, you can find x by plugging y into any of the two original equations. I will be plugging y into the first equation.

4x-3y=0

4x-3(4)=0

Simplify.

4x-12=0

Add 12 to both sides.

4x=12

Divide 4 to both sides to isolate x.

x=3

There you have it! Using the linear combination method, x=3 and y=4!

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