8/2/2019 Review - Algebra Essentials and Systems of Equations

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Algebra Essentials and Systems of Equations Review

Complete the following questions on separate paper. Check some of your answers

by using your calculator (the graphing method). Check the rest of your answers by

substituting your solution back into both equations to confirm that it is a point on

both lines, or by using some other appropriate method.

1. Solve the following systems of equations:a) 3x 2y = 3 b) 2y = 3x + 1 c) 3x 2y = 1

4x + y = 15 y x = 2 5x + 2y =

7

2. The sum of 2 numbers is equal to 60. The bigger number doubled minus the

smaller number is 82.5 Write 2 equations and then solve to find the 2 numbers.

3. Find the equation of the line joining the points (2 , 3) and (-3 , 6).

4. Draw a grid from -10 to 10 on each axis. Then plot the following lines:

a) y = 8 b) y = -x c) y = 3x 4

d) 2y + 3x = 12 e) x = -9 f) 3x = 12 3y

5. Find the equation of the line that is parallel to y = 2x + 5 and that goes throughthe point (2 , 9).

6. Find the equation of the line that is perpendicular to 2y 3x = 8 and that goes

through the point (6 , 12).

7. Solve the following systems of equations:

a) 4y 3x = 0 b) 3x + 5y = 4 c) y = x + 22y = x + 2 5x 2y = -14 3y 3x = 8

8. 3 books and 4 pens cost 1600 PhP. In the same shop 2 books and 5 pens cost

1300 PhP. Write 2 equations to show this situation. Define your variables clearly

and specifically. Solve to find the cost of 1 book.

8/2/2019 Review - Algebra Essentials and Systems of Equations

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9. Write down the equations of 2 lines that are perpendicular to each other and that

both go through the point (4 , 3).

10. Solve the following equations for x:

a) 3x 4 = x + 9 b) 2(x 3) = 4x 6

c) 3(2x + 4) = 12 3x d) 3x/2 5x/2 = 5

11. Make x the subject of these equations: a) y = 2(3 x) b) y 3x = Ax + 5B

12. A movie theater sells tickets for $9.00 each. Senior citizens receive a discount

of $3.00. The theater computers kept track of how many tickets were sold (636

total) and how much revenue was taken in ($4974 total), but they did not keeptrack of how many regular tickets were sold and how many senior tickets

were sold. The manager wants to know this information and so, knowing that

you are in Int 2 math, he asks you to figure out how many regular tickets were

sold and how many senior tickets were sold.

13. To earn extra money for her family, Nicole is making and selling earrings. Her

weekly costs for advertising, a space in the market, and transportation total

1500 PhP. Also, it costs 100 PhP for the materials to produce each pair of

earrings. If Nicole sells the earrings at 350 PhP per pair, how many pairs must

she sell per week to cover her costs and to start making money? Solve thisproblem using any method a table, equations, a graph, or another method of

your choosing.