Best Practice #Unit 1/2 – General Mathematics
Linear Relations and Equations
Question:
Solve this system of equations using the method of substitution (and check):
3y - 2x = 11
y + 2x = 9
Step
Method/ Hint
To solve by substitution, solve one of the
equations for either "x = " or "y = "
Step 1
Answer
3y - 2x = 11 ----1
y+2x = 9 ------2
Label each equation as ----1 and ------2
Rearrange the second equation to make y the
subject, creating a third equation in the form
Step 2
"y =" and label it ------3
NOTE: making y the subject in the second
equation was the simplest to transpose as the y
had no co-efficient
Substitute the "y" value (equation 3) into the
Step 3 original equation (equation 1).
IE. Replace the "y" value in the first equation by
what "y" now equals.
Further Maths
y+2x = 9 ------2
y+2x -2x = 9 -2x
To eliminate the ‘+2x’ you need to -2x from both sides
of the equation, eliminating the +2x from the LHS
y = 9 - 2x ------3
3y - 2x = 11 ----1
3(9 - 2x) - 2x = 11
Substitute 3 into 1
Best Practice #Unit 1/2 – General Mathematics
Solve this new equation for"x".
Step 4
Making sure to
1. Expand brackets
2. Combine like terms (underlining will
assist with this)
3. Move the terms, not associated with x,
to the other side of the equal sign
ensuring you do the inverse operation
Substitute this new "x" value into either of the
ORIGINAL equations in order to solve for "y".
Step 5 NOTE: Pick the easier one to work with- in this
case equation 2. Use this equation as y has no
coefficient
Step 6
Further Maths
Check: substitute x = 2 and y = 5 into BOTH
ORIGINAL equations.
If these answers are correct, LHS=RHS, both
solutions will be true!
3(9 – 2x) – 2x = 11
(27 - 6x) - 2x = 11
27 - 6x - 2x = 11
(Expand brackets)
(Collect like terms: underlined)
To eliminate the ‘+27’ you
need to -27 from both sides
of the equation
27- 27 - 8x = 11 -27
-8x = -16
-8x /-8 = -16 /-8
x=2
y+2x = 9
------2
To eliminate the ‘-8’ you need
to ÷-8 from both sides of the
equation
substitute x=2 into equation 2
y + 2 (2) = 9
y+4=9
y +4 - 4 = 9 – 4
y=5
3y - 2x = 11
3(5) - 2(2) = 11
15 - 4 = 11
11 = 11
y + 2x = 9
5 + 2(2) = 9
5+4=9
9=9
----1
(LHS=RHS)
(LHS=RHS)
Best Practice #Unit 1/2 – General Mathematics
Further Maths