Solving Systems by Graphing

Solving Systems of Equations by Graphing

What is a system of equations?

• A system of equations consists of two or more equations

• Ex 1: y = 3x + 5 & y = -4x - 2 

• Ex 2:  3x + 2y = 2 &  y = x + 5  

• Ex 3: y = 2^x & y = 4

Solutions to a System

• The solution to a system of equations is an ordered pair (x , y) that makes BOTH equations true.

• Graphically, the solution is the point of intersection.

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Multiple Choice

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

Multiple Choice

The solution is:

• (4, 3)

• (3, 4)

• (-4, 3)

• No solution

Multiple Choice

What is the solution?

• (6, 3)

• (3, 6)

• (-6, 3)

• No solution

Multiple Choice

This system has _____ solutions

• 0
• 1
• 2
• Infinitely many

Multiple Choice

How many solutions does the system have?

• Zero/None Solutions

• One solution

• Infinitely Many Solutions

Multiple Choice

When you graph the exact same equation twice,

• you will have no solution.

• you will have one solution.

• you will have infinite solutions.