Systems of Equations: Graphing & Substitution Method

Systems of Equations: Graphing & Substitution Method

Types of Solutions

• One Solution

• No Solution

• Infinite Solutions

Multiple Choice

What is the solution?

(Hint: Both lines are graphed over each other)

• One Solution

• No solution

• Infinitely Many Solutions

Multiple Choice

How many solutions does the graph have?

• One solution

• No solution

• Infinite solutions

Multiple Choice

How many Solutions?

• One Solution

• No solution

• Infinitely Many Solutions

• (0, -1)

Writing equations of lines from a graph

• Slope intercept form - y=mx+b

• M = Slope RISE/RUN

• Rise - Up and Down

• Run - Right or Left

• b = y intercept

Multiple Choice

Write the equation for the given line.

y = mx + b

• y = 2/3x + 5

• y = -2/3x + 5

• y = 5x + 2/3

• y = -5x - 2/3

Solve by GRAPHING

Graph using y = mx + b.

FIND the POINT OF INTERSECTION!

Multiple Choice

What is the solution to this system? 

• (3,1)
• No solution
• Infinite solutions
• (1,3)

Standard Form - to - Slope Intercept Form

What is the

slope-intercept form

of the equation

-8x+2y=4

Add 8x to both sides

Divide both sides by 2 (coefficient of y)

Solve by SUBSTITUTION

• Use your EQUATION solving skills!

• Take it STEP-BY-STEP

• You CAN do this!

Multiple Choice

Solve:

y=8x+1

y=6x+3

• (1, 9)

• (4, 14)

• (0, 1)

• (2, 4)

Multiple Choice

Solve the following systems of equations using substitution:

y = 8

y = -4x + 4

• (8, -1)

• (-28, 8)

• (-1, 8)

• (8, -28)

Solving equations with Substitutions

Solve using substitution:
y = -6x + 5
-2x + y = 5
1. Substitute (-6x + 5) for y in the second equation; -2x-6x+5=5
2. Solve second equation for x; -8x+5=5, -8x=0, x=0

3. Substitute the new x value(0) into the first equation; y=-6(0)+5, y=0+5, y=5
4. Solution is (0,5)

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