Use the method of substitution to solve the system of linear equations.  2x - y = 5 9x - 4y = 22 The solution is ? (Type an ordered pair.)Algebra One

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hkj1385's profile pic

hkj1385 | (Level 1) Assistant Educator

Posted on

Given :-

2x - y = 5........(1)

9x - 4y = 22.........(2)

Multiplying (1) by 4 we get,

8x - 4y = 20 .....(3)

On performing (2) - (3) we get

x = 2

Putting the value of 'x' calculated above in (1) we get

4x - y = 5

or, y = -1

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Solve the system `2x-y=5;9x-4y=22` :

When using substitution, we solve one of the equations for one of the variables. Choose to solve the first equation for y. (Why? It will be slightly easier since the coefficient of y is -1. You could choose to solve either equation for x if you wanted.)

`2x-y=5==>2x=y+5==> y=2x-5`

Now we can substitute this expression for y in the second equation:

`9x-4y=22`

`9x-4(2x-5)=22`

We have a linear equation in one variable. Solving we get:

`9x-8x+20=22`

`x=2`

Since y=2x-5 we have y=2(2)-5=-1.

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The solution is (2,-1)

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Checking we see that `2(2)-(-1)=5` and `9(2)-4(-1)=18+4=22` as required.

We can also graph:

Sources:
katehackett's profile pic

katehackett | High School Teacher | (Level 2) Adjunct Educator

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When you are given two equations, you want to isolate one of your variables. IE:

 

2x-y=5, let's isolate x.

2x=5+y

x=(5+y)/2

 

Now plug it into your second equation.

 

9((5+y)/2)-4y=22

 

You can solve for y.

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