Create Systems of Equations

AJ was asked to find the solution to this system of equations. x = 7 - 2y 2x + y = 5 Noticing that x was isolated and set equal to 7 - 2y, he decided to replace x in the second equation with its value. What method is AJ using and what equation did he write?

• Elimination; 2(7-2y) + y = 5

• Graphing; 2x = (7-2y) + y = 5

• Substitution; 2(7-2y) + y = 5

• Substitution; x = 7 - 2y + 2x + y = 5

Kayla solved the following system and found the solution to be (10, -9). x = -3y - 17 2x + 3y = -7 What would the graph of this system look like?

• A point on the coordinate plane

• Parallel Lines

• Coincident Lines (lines that graph one on top of the other)

• Lines that intersect at one point

How many solutions are there in the system of equations?

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

What is the first step Terri could take to find the solution to the system of equations using the Elimination Method?

• Multiply by -1 through one equation to flip the signs and create opposite y-values.

• Multiply by -1 through one equation to flip the signs and create opposite x-values.

• Multiply by 1 through one equation to flip the signs and create opposite y-values.

• Isolate a variable and substitute the value in the other equation.

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

________________ are two or more equations that have the same variables and work together.

• graphing lines

• elimination method

• system of equations

• table

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total. Solve the system:
x + y = 21
6x + 4y = 104

• (10, 11)

• (12, 9)

• (11, 10)

• (9, 12)

Solve by elimination:
4x+9y=28
-4x-y=-28

• (-7,0)

• (6,0)

• (-6,0)

• (7,0)

Solve by elimination:
3x+7y=23

-3x-7y=-17

• No solution

• ARN

• (-3,3)

• (3,3)

Solve by elimination:
-x+2y=17

2x+2y=-10

• ARN

• (-9,4)

• (-9,-4)

• (9,-4)