Solve Each System by Substitution – Quiz
Instructions: Solve each system by substitution in the quiz that follows. After using the substitution method, check your answers. You may want to view the examples in the next section first.
[WpProQuiz 30]
Solve Each System by Substitution – Step by Step
We can use the substitution method for simultaneous equations. This method helps us solve each system by substitution.
What is the Substitution Method?
We use the substitution method when we substitute numbers for variables in an algebraic expression or formula.
Substitution Method – Example
Study the example below that shows how to use the substitution method in systems of equations.
Example: Solve for x and y if 3x + 2y = 4 and x + 4y = 3
Answer: x = 1 and y = 1/2
Step 1: Label the equations
Label the equations A and B.
(A) 3x + 2y = 4
(B) x + 4y = 3
Step 2: Isolate one of the variables
To use the substitution method, we need to isolate one of the variables.
We will isolate variable x in equation B in this example.
x + 4y = 3
x + 4y – 4y = 3 – 4y
x + 4y – 4y = 3 – 4y
x = 3 – 4y
Step 3: Substitute the value of the isolated variable
Next, you need substitute the value of the variable you have isolated.
We have just determined that x = 3 – 4y.
So, now we substitute 3 – 4y for the value of x in equation A.
Equation A is 3x + 2y = 4.
3x + 2y = 4
3(3 – 4y) + 2y = 4
Step 4: Perform the multiplication
3(3 – 4y) + 2y = 4
(3 × 3) – (3 × 4y) + 2y = 4
9 – 12y + 2y = 4
Step 5: Perform inverse operations to solve for y
9 – 12y + 2y = 4
9 – 9 – 12y + 2y = 4 – 9
9 – 9 – 12y + 2y = 4 – 9
–12y + 2y = 4 – 9
–12y + 2y = –5
–10y = –5
–10y ÷ –10 = –5 ÷ –10
y = 1/2
Step 6: Substitute the value of y to solve for x
Finally, we need to substitute the value of y into equation A to solve for x.
We know that equation A is 3x + 2y = 4 and that y = 1/2.
So, substitute the value of y.
3x + 2y = 4
3x + (2 × 1/2) = 4
Then perform the operations to solve for x.
3x + (2 × 1/2) = 4
3x + 1 = 4
3x + 1 – 1 = 4 – 1
3x + 1 – 1 = 4 – 1
3x = 4 – 1
3x = 3
3x ÷ 3 = 3 ÷ 3
x = 1
Substitution Method in Expressions
You will see several questions on your algebra test that ask you to solve an algebraic expression by substituting the value of x or another unknown variable.
Example: What is the value of 4(3x + 12) when x = 5?
Answer: 108
STEP 1: Substitute the value of the variable.
4(3x + 12) =
4[(3 × 5) + 12]
STEP 2: Perform the operations to solve.
4[(3 × 5) + 12] =
4[(15) + 12] =
4(27) =
4 × 27 = 108
Substitution Method in Formulas
You will also see problems on your algebra exam that ask you to use the substitution method in a formula.
In addition, you will need to use the substitution method in this way on the geometry part of the exam.
Example: The area of a triangle is A = (base × height) ÷ 2. What is the area of a triangle that has a base of 8 units and a height of 6 units?
Answer: 24 units
STEP 1: Substitute the values into the formula.
A = (base × height) ÷ 2
A = (8 × 6) ÷ 2
STEP 2: Perform the operations to solve.
A = (8 × 6) ÷ 2
A = 48 ÷ 2
A = 24
Further Algebra Practice
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