5.2 Solving Systems by Substitution

Solving Systems By Substitution​

​TAKE NOTES!!

Multiple Choice

Warm up: #1

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

Multiple Choice

Warm up: #2

What is the solution to this system of equations?

• (4, -1)

• (-1, 4)

• (-4, 1)

• (-4, -1)

Match

Warm up: #3

Match the solution to the system of equations.

(-2, -1)

(2, -1)

(1, 4)

(-4, -1)

• (-2, -1)

• (2, -1)

• (1, 4)

• (-4, -1)

Multiple Choice

Warm up: #4

Which of the following shows the solution to the system?  y= -1/4x + 4 y = 2x + 2

• A

• B

• C

• D

A system is two or more equations that share variables.

The solution to a system is the point where the two lines intersect. All answers should be writen as ORDERED PAIRS!!

The solution would be (4, -1).

One Solution

The answer would be no solution since the lines a parallel and will never touch.

​

When solving you will get two numbers that don't equal each other. EX: 3=9

​

No Solution

The answer is all real solutions because the two equations create the same line.

​

​When solving you will get two numbers that equal each other. EX: 0=0

All Real Solutions

​Remember......

Steps For Solving By Substitution

Step 1: Solve 1 equation for 1 of the variables.

x=___ or y=____​

​

Step 2:​ Substitute x =___ or y = ___ from the first step into the other equation and solve for the variable.

​

​Step 3: Substitute your answer into one of the original equations and solve for the other variable.

​

Step 4: Write your answer as an ordered pair.​

​

Step 1: One of your equations is already set up as x=_____ or y=_____.

In fact, they both are.​

​

Step 2: Substitute y=-4x+8 into the other equation for y.​

​Equations:

y= -4x + 8 y= -3x+5

Step 2 continued: solve for x.

​

Step 3: substitute x= 3 into one of your original equations and solve for y.

​

​

​

​

Step 4: write your answer as (3, -4)​.

​

​

​

​

Try: y=2x + 1 and 3x+y=11

​Solve each system using substitution

Multiple Choice

y = -2x + 18
y = 8

• (5, 8)

• (-5, 8)

• (2, 8)

• (-2, 8)

Multiple Choice

Solve the system by substitution.
 
5x + 4y= −14
y =  −7x  −  15 

• (-2, -1)

• (1, -2)

• (-2, 1)

• (-1, -2)

Multiple Choice

Solve this system of equations. 
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

Multiple Choice

x + 2y = 2
x = -4y + 2

• (-3, 0)

• (0, 2)

• (-3, -2)

• (2, 0)

Multiple Choice

x - 3y = -13
4x + 2y = 4

• (1, 4)

• (-1, -4)

• (-1, 4)

• (1, -4)