# TOPIC # 8 – 4: Solving Systems of Equations by Substitution

```Solutions:
1. x2 = x + 30
Solutions:
2. 3x2 – 8 = 10x
Solutions:
3. x2 - 2x = 0
Set equation = 0
Factor Completely
Set each factor = 0 and solve.
Set equation = 0
Factor Completely
Set each factor = 0 and solve.
Set equation = 0
Factor Completely
Set each factor = 0 and solve.
Solution
4. 8x + 24 &lt; 2x2
Solutions
5. x&sup2; + 4x + 3 &lt; 0
Equation
6. Roots are at
x = -5 and x = -2/3
function
Set equation = 0
Set equation = 0
Set the equations = 0
Factor Completely
Factor Completely
Remove any fractions by
multiplying the equation by the
denominator
Set each factor = 0 and solve.
Test a point to determine
Set each factor = 0 and solve.
Place in Factored Form and
multiply out
Sage-N-Scribe Kagan Activity:
Problem 1 - Student A is the Sage; Student B is the Scribe.
1. The Sage gives the Scribe step-by-step instructions on how to solve problem #1
2. The Scribe records the Sage’s solution step-by-step in writing
3. If the Sage is correct, the Scribe praises the Sage. Otherwise, the Scribe
coaches, then praises.
4. Students switch roles for the next problem. (at the end, each student will
have one problem worked out on their paper, which they will glue in their notebook)
#1.
#2.
x2 + 8x = -15
12x2 + x = 1
```