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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
1.21 Linear Equations in Two Variables- Solving by the Method of Substitution

Method:
  1. Solve one of the equations for one variable in terms of the other.
  2. Substitute that expression found in step 1 into the other equation to obtain an equation in one variable.
  3. Solve the equation obtained in step 2
  4. Back substitute the solution in step 3 into the expression obtained in step 1 to find the value of the other variable
  5. Check that the solution satisfies each of the original equations
Example:
Solve the same system of equations by the method of substitution.
2x + y = 4 ----- Equation 1
x − y = −1 ------- Equation 2
Solution:
Take equation 1: 2x + y = 4 ----- Equation 1
2x + y = 4
y = 4 - 2x
Substituting y in equation 2
x − y = −1 ------- Equation 2
x − (4 − 2x) = −1
Solving for x
x − 4 + 2x = −1
3x = −1 + 4
3x = 3
x = 1
To find y, substitute x = 1 in equation 1 2x + y = 4 ----- Equation 1
2x + y = 4
2(1) + y = 4
2 + y = 4
y = 4 - 2
y = 2
x = 1 and y = 2
Answer: (1,2)
Directions: Solve the linear equations by the method of substitution. Also write at least 5 examples of your own.
Q 1: Solve the system by the method of substitution
x − y = 2
2x + y = 10
(4,2)
(2,3)
inconsistant
(2,4)

Q 2: Solve the system by the method of substitution
2x + y = 6
-x + y = 0
(4,2)
(1,0)
(2,2)
(2,3)

Q 3: Solve the system by the method of substitution
x - 3y = -2
5x + 3y = 17
(1/2.2/3)
(4/3,5/3)
(5/2,3/2)
inconsistant

Q 4: Solve the system by the method of substitution
7x + 2y = 16
21x 6y = 24
(4,9)
inconsistant
(13,9)
(3,-4)

Q 5: Solve the system by the method of substitution
x + y = 4
x - y = 2
(1,4)
(3,1)
inconsistant
(2,1)

Q 6: Solve the system by the method of substitution
2y + x = 3
4y 3x = 1
(0,2)
(1,1)
(1,7)
inconsistant

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Question 8: This question is available to subscribers only!


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