Practice Worksheet for Elimination and Substitution

Use either the method of Substitution or Elimination to solve each of the following equation sets:

1. 3x+y=5
2. 4x-2y=7

1. -y+2x=19
2. 3x-4y=25

1. 5y+25x=105
2. 10y-18x=97

1. 2x=6-y
2. y=8-2x (hint: before solving either equation, get the variables on the same side of the equation)
   

Elimination

If you are given a problem in which there are 2 variables and 2 equations, you can solve it through elimination. If for example you are given:

10x+6y=46 and 5x-2y=18

It would be very effective to use substitution in this case. With elimination, you are looking to "eliminate" one of the variables. So in this case, we look to see which variable would be easier eliminate, and it happens to be y.

If we look at all of the variables on one side of the equation and the answers on the other, we can eliminate y by multiplying all of the parts of the second equation by 3.

10x+6y=46

5x-2y=18

10x+6y=46

3(5x)3(-2y)=3(18)

and you end up with...

10x+6y=46

15x-6y=54

Now because we have all of the variables on one side, we can add the equations and have both 6y and -6y cancel each other out. Remember that when canceling variables out, they must have opposite signs. If opposite signs are not given, then you must multiply one of the equations by (-1) to get a negative sign and thus be able to add the equations.

what is left is:

10x+15x=46+54

We can combine the two terms on the left and the two terms on the right and we end up with:

25x=100

We then know that x=4, and we can plug that into either of the original equations to find the value of y.

10x+6y=46 ----> 10(4)+6y=46 ----> 40+6y=46 ----> 6y=6----> y= 1

Substitution Method

if you are given a problem in which there are 2 variables and 2 equations, there are many ways to solve for the variables. One method is called the method of substitution.

for instance if your two equations are:
1) x+2y=8
2)2x+6y=20
You can use the method of substitution----------

Steps:

1) 2y=7-x (by subtracting x from both sides)
2) y=4-0.5x (dividing both sides of the equation by two)
3) We can plug (4-0.5x) back into the 2nd equation to get:
4) 2x +6(4-0.5x)=20 (because y is equal to 4-0.5x, we can plug that y value into the 2nd equation)
5)2x+24-3x=20 (using the distributive property)
6) -x+24=20 (combining like terms)
7)-x=-4 (subtract 24 from both sides of the equation)
8)x=4 (multiply everything by -1)
Now, you can plug the x value into either one of the original equations.
9) (4)+2y=8 (the x value of 4 was plugged into equation #1)
10)2y=4 (subtract 4 from each side)
11) y=2 (divide both sides of the equation by 2)
Now, you have figured out both your X and Y value. To check this answer you can plug both values into either equation and see if it matches the given outcome.
12) (4)+2(2)=8 (the X and Y values were plugged in)
13) 8=8 (your answer has been checked!!)

QUESTIONS

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Quadratic Equation

If solving for X in any equation where X is being squared, for example 2x²+4x+2, you can use the quadratic formula.

x= (-b)±√(b²-4ac)
(2a)

'a' is the coeffecient of X², so in this case a=2. b is the coeffecient of X, so in this case b=4. C is the 'plain' number at the end of your equation, so in this case c=2.

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