Download Solving Systems of Equations Graphically

Lesson 8.1: Solving Systems of Equations Graphically
Specific Outcome: Solve, algebraically and graphically, problems that involve systems of linear-quadratic and
quadratic-quadratic equations in two variables. (Relations and Functions: 6) (Achievement Indicators ~ 6.1 - 6.7)
A system of equations is two or more different equations involving the same variables. Determining the
solution to a system of equations means determining point(s) that are common to both equations. A
common point is called a point of intersection.
Example 1: Solve the following system of equations graphically. Once you’ve determined the point(s) of
intersection, remember to check the ordered pair(s) in both of the original equations.
𝑦 + 3𝑥 2 − 2𝑥 − 4 = 0
Check:
𝑦+𝑥+2=0
Example 2: Solve the following system of equations graphically. Once you’ve determined the point(s) of
intersection, remember to check the ordered pair(s) in both of the original equations.
𝑦 − 3𝑥 2 + 12𝑥 = 16
Check:
2
𝑦 + 4𝑥 − 16𝑥 = −12
Example 3: Two numbers have a sum of 17. The square of the first number plus 5 equals the second
number. What are the two numbers?
Example 4: For the linear-quadratic system of equations shown below, write the linear equation and
quadratic equation that would result in this solution.
y
12
11
10
9
8
7
6
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
9
10
11
x
–2
–3
–4
–5
–6
Practice Questions: Page 435 # 2, 3, 4(a, e), 5(a, e), 9