Solving Systems of Equations (graphing and substitution)

Solving Systems of Equations by Graphing

We can solve the system of equation by graphing each equation and finding their intersection point.

• y = 2x + 3

• y = -3x + 4

One Solution

When you graph both equations they will cross in exactly ONE POINT. The INTERSECTION POINT is the ANSWER to the system.

No Solution

When you graph both equations they NEVER intersect. No intersection point means no solution.

Infinite Solutions

When you graph both equations and they overlap. When the lines overlap at every point it means they have infinite solutions. They are actually the same line.

Multiple Choice

If you graph 2 lines and they intersect at ONE point, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None of These

Multiple Choice

If 2 lines never intersect, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None Of These

Multiple Choice

If a system has 2 lines that overlap, meaning they share all of the same points, how many solutions does the system have?

• No Solution

• Infinite Solutions

• One Solution

• None Of These

Multiple Choice

The solution to a system of equations is any ordered pair that makes both equations true. 

• TRUE
• FALSE

Multiple Choice

A system of linear equations is... 

• Math Magic

• One Equation

• Always more than 2 equations

• A set of 2 or more equations

Multiple Choice

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

Multiple Choice

How many solutions will this system have?

• One

• Two

• No Solution

• Infinitely Many Solutions

Multiple Choice

If a system of equations has no solution, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

Multiple Choice

What is the solution?
(Hint:  Both lines are graphed over each other)

• One Solution

• No solution

• Infinitely Many Solutions

Multiple Choice

This system has _____ solutions

• no
• 1
• 2
• Infinitely many

Multiple Choice

Lesly graphed two lines in order to find the solution to a given system of equations.

What is the solution?

• (-3,-8)

• (-8,-3)

• (3,-8)

• (8,3)

Multiple Choice

These two lines intersect at _____.

• (4, -2)

• (4, 2)

• (-2, 4)

• No solution

Multiple Choice

The solution to this system of equations is:

• (4, 3)

• (3, 4)

• (-4, 3)

• No solution

Multiple Choice

Solve the system of equations by graphing.

(Use desmos.com to help)

• (4, 7)

• (3, 5)

• (6, 7)

• (5, 3)

Multiple Choice

Solve the system of equations by graphing.

(Use desmos.com to help)

• (0, 3)

• (5, 5)

• (-4, 6)

• (6, -4)

Multiple Choice

Solve the system of equations by graphing.

(use desmos.com to help

• No Solution

• (-2, 6)

• (4, 0)

• (2, 2)

Multiple Choice

Solve the system by substitution. 

(write equations equal and the solve - practice using the equations - don't graph) y = 2x − 11 

y = -2x + 5

•  (4,-3)

• (-4,13)

• (-4,-3)

• Infinite number of solutions  

Multiple Choice

Solve the system by substitution. 

(write equations equal and the solve - practice using the equations - don't graph) y = 2x + 5

y = -x + 2

• (1, 7)

• (7, 1)

• (2, 9)

• (-1, 3)

Multiple Choice

Solve the system by substitution. 

(write equations equal and the solve - practice using the equations - don't graph) y = 2x + 1 y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Fill in the Blank

Solve the system by substitution. 

(write equations equal and the solve - practice using the equations - don't graph) y = 7x + 9

y = -x - 7

Write your answer as a coordinate pair (x, y)

Fill in the Blank

Solve the system by substitution. 

(write equations equal and the solve - practice using the equations - don't graph) y=8x+1 y=6x+3

Write your answer as a coordinate pair: (x, y)

Open Ended

If a system of equations has no solutions what must be true about the equations in the system?

Open Ended

On a scale of 1 to 10, with 1 being the lowest and 10 the highest, how do confident do you feel about solving a system of equations using the graphing method?

Open Ended

On a scale of 1 to 10, with 1 being the lowest and 10 the highest, how do confident do you feel about solving a system of equations using the substitution method?