Systems of Linear Equations

Solving Systems of Linear Equations: Vocabulary

100

What is the first step in solving a system with linear equations by substitution? Fill in the blank. Isolate the ________.

y

200

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

Graphing and Substitution

300

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

Ordered pair

400

Daily Double: What's your wager?

What is a set of two or more linear equations called?

500

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

Infinite Solutions

Substitution Method

100

Is (1,0) a solution to the following system of equations? y=1 y=x Show your work

No

200

Is (5,2) a solution to the following system of equations? y=2 3x-5y=5 Show your work.

Yes

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

Daily Double: What's your wager? Wager:______

Graph y=-4 and describe the slope.

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+2y=2

Answer: y=-2x+1

400

Convert to slope intercept form: 3x+9y=-18

y=-3x-2

500

Convert to slope intercept form: 5x+4y=-12

Answer: -4/5x-3

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

Identify step 2 when solving a system of linear equations with substitution: _________ the first equation in y of the second equation

Substitute

500

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

solution