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)

Fill in the Blanks

Write 2x + 4y = 12 in slope intercept form. Leave slope in fraction form. REMEMBER: "Add or subtract the x-term, Divide by the 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)

Next Steps

• Complete the quiz using the code provided in chat. Go to joinmyquiz.com

• Complete your Delta Math work! If you cannot sign in, you need to let us know!!! REMEMBER your user name is your school email and your password is your first initial last initial and your ENTIRE lunch number.