1. Solving Linear Systems by Graphing
5.1
Solving Linear Systems by Graphing
Objective 1 – Solve a system of linear equations by graphing
Essential Question: How do you find a solution for two linear equations in two variables?

2. System of Equations: are two equations considered together as one question.
Ex: x + y = 7
2x – 3y = 4
Solutions to Systems are the ordered pairs (x,y) that make both equations true
The solution to above system is (5,2)
5 + 2 = 7
2(5) – 3(2) = 4

3. Solving a system by graphing
EXAMPLE
Solving a system by graphing
Graph both lines to see where they intersect
The lines intersect at (2,-1)

4. EXAMPLE Solve the system x + y = -2 2x – 3y = -9
Write each equation in slope intercept form, then graph
x + y = -2
– x – x
y = – x – 2
2x – 3y = – 9
– 2x – 2x
–3y = – 2x – 9
– – 3 – 3
y =
The lines intersect at (-3, 1)

5. Check the coordinates algebraically by substituting (-3,1) into each equation of the original linear system.
x + y = -2
= -2
-2 = -2
2x – 3y = -9
2(-3) – 3(1) = -9
-6 – 3 = -9
-9 = -9