Hopefully this may help you kids!!!!

1. SOLVING SYSTEMS OF
LINEAR EQUATION IN TWO
VARIABLES
(SUBSTITUTION METHOD)

2. SYSTEMS OF LINEAR EQUATION
• Two or more linear equations.
• A SOLUTION to a system of linear
equations in two variables consists of
an ordered pair that satisfies both
equations.

3. SUBSTITUTION METHOD
• Solve for one of the variables in one
of the equations and then substitute
that variable in the other equation.

4. Example:
𝒙 + 𝟑𝒚 = −𝟒 Equation 1
𝒙 − 𝒚 = 𝟏𝟔Equation 2
STEP 1: Solve one of the equations either "x= “ or "𝒚 = “.
Using Equation 1, find the value of x.
𝒙 + 𝟑𝒚 = −𝟒
− 𝟑𝒚 = −𝟑𝒚
𝒙 = −𝟑𝒚 − 𝟒(partial
value of x)

5. STEP 2: Substitute the expression into
the other equation.
Note: We used Equation 1 to get
Substitute the partial value of 𝒙to Equation 2to
find the value of 𝒚.
𝒙 − 𝒚 = 𝟏𝟔Equation 2
−𝟑𝒚 − 𝟒 − 𝑦 = 16
−𝟑𝒚 − 4 − 𝒚 = 16
−𝟒𝒚 − 4 = 16
𝟒 = 𝟒
−𝟒𝒚
−𝟒
=
𝟐𝟎
−𝟒
𝒙 = −𝟑𝒚 −
𝟒(partial value of
x)
𝒚 = −𝟓
(value of y)

6. STEP 3: Using the expression obtained
in step 1, SUBSTITUTE the value of the
variable obtained in step 2.
• NOTE: In Step 1, we get
and in Step 2, we found that
𝒙 = −𝟑𝒚 − 𝟒
= −𝟑 −𝟓 − 𝟒
= 𝟏𝟓 − 𝟒
𝒙 = −𝟏𝟏
So, the solution set is (−𝟏𝟏, −𝟓).
𝒙 = −𝟑𝒚 − 𝟒(partial
value of x)
𝒚 = −𝟓
(value of y)