Math 8 Chapter 5

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 and Word Problems

100

Solve the system of linear equations:

y = 2x - 2

y = 2x + 9

No solution.

200

Nikki bought hamburgers and hot days.  She purchased 5 hamburgers and 5 hot dogs , and spent $50.  Amanda bought 3 burgers and 7 hot dogs and spent $46.  How much was a burger and how much was a hot dog?

Burgers cost $6 and Hot dogs cost $4

300

A farmhouse shelters 10 animals. Some are pigs and some are ducks. Altogether there are 36 legs. How many of each animal are there?

2 ducks and 8 pigs

400

Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?

2 fancy

5 plain

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

3x - 14 = 7y

y= 3/7 x-2

300

reflect the point A( 4, 7) over the y-axis.

A' (-4,7)

400

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

(0,0) and (2,6)

y = 3x

500

Write an equation of a line that has a slope of 4 and passes through the point (-3, 6)

y= 4x +18