Systems of Equations Review

Equal Values

100

What is one reason that you would choose to solve by equal values?

Both equations are solved for the same variable.

200

y=x+3

y=2x+5

(-2,1)

300

x=2y-4 

x=-8y+16

(0,2)

400

x=y-8 

x=-y

(-4,4)

500

y=-2x-1 

y=x+5

(-2,3)

Substitution

100

What is one reason that you would choose to solve by substitution?

1 equation is solved for a variable.

200

y = -2

4x - 3y = 18

(3,-2)

300

2x - 3y = -1

y = x -1

(4,3)

400

y = -3x + 5

5x - 4y = -3

(1,2)

500

-3x - 3y = 3 

y = -5x - 17

(-4, 3)

Elimination

100

-4x-2y=-12

4x+8y=-24

(6,-6)

200

-6x + 5y = 1

6x + 4y = -10

(-1, -1)

300

7x + 2y = 24

8x + 2y = 30

(6, -9)

400

5x + y = 9

10x - 7y = -18

(1,4)

500

You and a friend go to Tacos Galore for lunch. You order two soft tacos and three burritos and your total bill is $13.00. Your friend's bill is $12.00 for four soft tacos and two burritos. How much do soft tacos cost? How much do burritos cost? 

Let x = soft tacos    Let y = burritos

Write equations to represent you and your friend, then use the equations to solve for x and y.

You:  2x+3y=13

Friend:  4x +2y= 12x

x= $1.25     y=$3.50

You Pick the Method

100

What method would you use if you had the following system of equations?

 y=x+5 

4x+y=20

Substitution (because the top equation is solved for y)

200

What method would you use if you had the following system of equations? 

-x+y=5

x-5y=-9

Elimination because when you add these, the x's cancel out.

300

8x + y = -16

-3x + y = -5

(-1, -8)

400

-4x + 9y = 9

x - 3y = -6

(9,5)

500

7x + 5y = 8

7x + 7y = 8

(8/7,0)

Systems Information

100

How many equations are in a system of equations?

2 or more

200

How should your answer be written when solving systems?

As an ordered pair (x,y)

300

How do you check your answer when solving systems of equations?

You plug the ordered pair back into both equations and see if you get the same number on both sides of the equals sign for both equations.

Graph it in Desmos

400

It is possible to have no solution to a system of linear equations. When graphing, what does that look like?

Two lines that are parallel and do not intersect.

500

It is possible to have infinitely many solutions to a system of linear equations? 

a) When solving by graphing what would that look like?

b) When eliminating what would happen?

Yes it is possible.

a) They would graph as the same line.

b) You would eliminate both variables and the constants and have 0=0.