TEST #4 Algebra II Pre-AP

ALGEBRA II PRE-AP Name:______SYSTEMS AND INEQUALITIES REVIEW Date:______Period:______

1. What is the x-coordinate of the solution to the system of linear equations below?  5x  9y  12  3x  2y  22

4. The length of a rectangle is equal to double the A. -6 C. -2 width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter B. 2 D. 6 is 42 centimeters?

l  w  2 l  w  2 A B 2l  4w  42 2(l  w)  42 2. Lauren has 5 more concert tickets than Kent. Angel has triple the number of concert tickets as Lauren. The three students have a total of 18 l  2w l  2w C D concert tickets. Which equation can be used to find 2l  4w  42 2(l  w)  42 how many concert tickets Kent has?

F x + 5x + 3x = 18 G x + (x+5) + 3(x+5) = 18 H x + (x+5) + 3(x) = 18 5. Which graph J x + 5x + 3(5x) = 18 best represents all the pairs of numbers (x, y) such that x  y  2 ?

3. In the system of equations -10x + 5y = -15 and -4x – 15y = -17, which expression can be correctly substituted for y in the equation 4x – 15y = -17?

A  3  2x B 15  2x C  3  2x D 15  2x

6. Explain in your own words what it means to “solve a system”. Solve the following system algebraically. Show your work and remember to check your solutions. 7.

For each of the following word problems, define your variables, set up a system, solve, and label your answers. 8. A person invests $7000 in treasury notes and bonds. The notes pay 6% annual interest and the bonds pay 8% annual interest. If the annual income from interest is $520, how much is invested in each area?

9. A grocer mixes together some peanuts costing $1.50 per pound, some almonds costing $2.25 per pound, and some cashews costing $3.75 per pound. The grocer sold 270 pounds of the mixture for $2.89 per pound. If there are ½ as many peanuts as there are cashews, how many pounds of each type of nut were in the mixture the grocer sold?

10. The length of a rectangle is 5 cm less than twice its width. If the perimeter is 80 cm, find the dimensions of the rectangle. Solve the following system of inequalities by shading the feasible region on the grid. 11. x  y  5   x  y  2  x  y  1  x  y  3

Solve the following system algebraically. Show all work and check your solution. 12.