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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

Middle/High School Algebra, Geometry, and Statistics (AGS)
1.19 Solving Equations - Elimination Method 1

Method of Elimination

Example:
Solve x + y = 6 and x - y = 2.

Solution:
In this method we eliminate one variable by addition or subtraction.
Given that x + y = 6 and x - y = 2.
In the above two equations, the coefficients of y are +1 and -1.  They have the same value and the signs are unlike.
If we add two equations the variable y will be eliminated.
x + y = 6--------1
x - y = 2--------2
Adding equations 1 and 2 we get

2x = 8

 
x = 8 / 2 = 4
Therefore, x = 4.
Substituting the value of x in the equation 1 or 2.
x + y = 6
4 + y = 6
y = 6 - 4
y = 2
Therefore, the solution set {(4,2)}.

Verification:
We have to verify the solution (4,2) if it satisfies both equations.  Substitute x = 4 and y = 2 in the equations.
x +  y = 6 and x - y = 2
4 + 2 = 6 and 4 - 2 = 2
Therefore, the solution (4,2) is correct.


Directions: Choose the correct answer. Also write at least ten examples of your own.
Q 1: Solve x + y = 11 and x - y = 5.
x = 8 and y =3
x = 7 and y = 6
x = 4 and y = 6
x = 3 and y = 8

Q 2: Solve x + y = 19 and x - y = 5.
x = 8 and y = 11
x = 11 and y = 8
x = 12 and y = 7
x = 7 and y = 12

Q 3: Solve x + y = 34 and x - y = 18.
x = 24 and y = 6
x = 26 and y = 8
x = 22 and y = 10
x = 20 and y = 12

Q 4: Solve x + y = 19 and x - y = 3.
x = 13 and y = 6
x = 11 and y = 8
x = 8 and y = 11
x = 12 and y = 7

Q 5: Solve x + y = 24 and x - y = 10.
x = 15 and y = 8
x = 17 and y = 7
x = 16 and y = 9
x = 14 and y = 6

Q 6: Solve x + y = 7 and x - y = 3.
x = 5 and y = 2
x = 2 and y = 5
x = 4 and y = 3
x = 3 and y = 4

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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