Systems of Linear Equations

Solving Systems of Linear Equations: Vocabulary

100

What is the first step in solving a system with linear equations? Fill in the blank. Identify the isolated ________.

Answer: Variable

200

What are the two methods to solving systems of linear equations that we have discussed so far?

Answer: Graphing and Substitution

300

The solution to a system of linear equations is always written as an ________ ________.

Answer: Ordered pair

400

Daily Double: What's your wager? The solution to a system of linear equations is also called this the POI. What does POI stand for?

Answer: The Point of Intersection

500

Lines that have the same slope and y-intercepts have how many solutions?

Answer: Infinite Solutions

Substitution Method

100

Solve the following system of equations by substitution: y=1 y=x Remember write your answer as an ordered pair.

What is x=1, y=1 or (1, 1)

200

Solve the following system of equations by substitution: y=2 3x-5y=5 Remember write your answer as an ordered pair.

What is x=5, y=2 or (5, 2)

300

Solve the system of equations by substitution: y= -4 2x-y=-6 Remember write your answer as an ordered pair.

What is x=-5, y=-4 or (-5, -4)

400

Solve the following system of equations using the substitution method: y=3x-5 y=7x-13

x = 2 and y = 1 or (2,1)

500

Use the substitution method to solve this system of linear equations: y=-7x-3 y=8x+12 Remember write your answer as an ordered pair.

Answer: (-1,4)

Graphing Method

100

Solve the following system of equations by graphing. Identify the number of solutions; One, (write answer as an ordered pair) None, or Infinite and why? y=3x-4 y=3x-4

Answer: No Solution because the slopes are the same. Therefore, the lines are parallel.

200

Solve the system of equations by graphing. y=-3/4x+2 y=1/4x-2 Remember write your answer as an ordered pair.

Answer: The solution is (4,-1)

300

Solve each system of linear equations by graphing. Identify the number of solutions: One (write as an ordered pair), None, or Infinite. y=-1/2x+3 y=-1/2x+3

Answer: Infinite solutions because the slopes and y intercepts are the same. (The equations are the same.)

400

Solve the system of linear equations using the graphing method. y=-1/3x-2 y=2/3x+1

Answer: (-3,-1)

500

Solve the system of linear equations using the graphing method. y=1/3x + 4  and   x=3 .

Answer: (3,5)

Convert to Slope Int. Form

100

Identify the slope in the this linear equation: y=2/3x-5

Answer: Slope =2/3

200

Identify the y-intercept in the following linear equation: y=-2x-6

Answer: y=-6 or (0,-6)

300

Convert to slope intercept form: 4x+y=2

Answer: y=-4x+2

400

Convert to slope intercept form: 3x+y=-18

y=-3x-18

500

Convert to slope intercept form: 6x+2y=-12

Hint: Don't forget to remove the coefficient from y.

Answer: -3x - 6

Short Answer

100

If both equations in a system have the different slopes and y intercepts, how many solution exist to the equations?

Answer: One solution

200

This word is used to describe "replacing" a number into an equation for a variable.

Answer: Substitute

300

If the slopes are the same but the y-intercepts are different, how many solutions are there? Why?

Answer: No solution because they don't intersect (they are parallel)

400

A system of linear equations that creates one line on a graph represents how many solutions to the system?

Answer: Infinite Solutions

500

Fill in the blank. The point of intersection is the same as the __________ to a system of equations.

Answer: solution