System of Linear Equations

Solving Systems of Linear Equations by Graphing

100

Solve the system of linear equations by graphing:

y = 2x + 9

y = -x + 6

(-1,7)

200

Solve the system of linear equations by graphing:

y = x + 4

y = -x + 2

(-1,3)

300

Solve the system of linear equations by graphing:

y = 2x + 5

y = 0.5x - 1

(-4,-3)

400

Solve the system of linear equations by graphing:

x + y = 7

y = x + 3

(2,5)

500

Is it possible for a system of linear equations to have exactly two solutions? Explain your reasoning.

No, two lines cannot intersect in exactly two points. 

Solving Systems of Linear Equations by Substitution

100

Solve the system of linear equations by substitution:

y = x - 4

y = 4x - 10

(2,-2)

200

Solve the system of linear equations by substitution:

y = 2x + 5

y = 3x - 1

(6,17)

300

Solve the system of linear equations by substitution:

x = 2y + 7

3x - 2y = 3

(-2, -4.5)

400

Solve the system of linear equations by substitution:

2x = y - 10

x + 7 = y

(-3,4)

500

Solve the system of linear equations by substitution:

y - x = 0

2x - 5y = 9

(-3,-3)

Solving Systems of Linear Equations by Elimination

100

Solve the system of linear equations by elimination:

x + 3y = 5

-x - y = -3

(2,1)

200

Solve the system of linear equations by elimination:

x - 2y = -7

3x + 2y = 3

(-1,3)

300

Solve the system of linear equations by elimination:

2x + 7y = 1

2x - 4y = 12

(4,-1)

400

Solve the system of linear equations by elimination:

2x - y = 0

3x - 2y = -3

(3,6)

500

Solve the system of linear equations by elimination:

x + 4y = 1

3x + 5y = 10

(5,-1)

Solving Special Systems of Linear Equations

100

Solve the system of linear equations:

y = 2x - 2

y = 2x + 9

No solution.

200

Solve the system of linear equations:

y = 3x + 1

-x + 2y = -3

(-1,-2)

300

Solve the system of linear equations:

y = 5x - 9

y = 5x + 9

No solution. 

400

Solve the system of linear equations:

y = 8x - 2

y - 8x = -2

Infinitely many solutions.

500

Describe and correct the error in solving the system of linear equations.

y = -2x + 4

y = -2x + 6

The lines have the same slope so there are infinitely many solutions.

The lines have the same slope but different y-intercepts so therefore they are never going to intersect = No Solution.

Miscellaneous

100

Solve the equation:

5(2 - y) + y = -6

y = 4

200

Write the equation in slope-intercept form:

 - 16 = 8y - 4x

y = 1/2x - 2

300

What is true about the two lines below? 

y = -3x + 4

y = -3x - 6

The two lines are parallel. 

400

Write an equation of the line that passes through the given points:

(0,0) and (2,6)

y = 3x

500

What is true about the two lines below? 

y = 2x + 4

y = -1/2x - 6

They are perpendicular.