Systems of equations Diagnostic Assessment

Name ______

Alg 7. Solve systems of linear equations and inequalities using graphs, substitution, and elimination

SHOW ALL WORKING

1. Solve by graphing

Alg 5. Write and use equivalent forms of equations (such as writing linear equations in slope-intercept form), and inequalities

Alg 7. Solve systems of linear equations and inequalities using graphs, substitution, and elimination

2. Solve the following system of equations

SHOW ALL WORKING

a. b.

c. d.

Alg 16. Solve multi-step linear equations and inequalities (including compound) using a variety of methods

Solve each system by graphing:

3. 4.

Alg 3. Model and solve real-life situations using linear (equations and inequalities), quadratic and exponential models through tables, graphs and algebraic representations

Meas 2. Solve simple problems involving rates and derived measurements for such attributes as velocity and density

Use a system of equations or inequations to model each situation. Solve by any method.

5. A chemist needs to mix a solution containing 30% insecticide with a solution containing 50% insecticide to make 200 liters of a solution that is 42% insecticide. How much of each solution does she need to use?

6. Suppose you bought supplies for a party. Four rolls of streamers and 15 party hats cost $42. Later you bought 2 rolls of streamers and 3 party hats for $12. How much did each roll of streamers and party hats cost?

7. On a canoe trip Tony paddled downstream (with the current). His speed relative to the bank of the river is 15 km./hr. During the return trip upstream (against the current) his speed relative to the bank is 11 km./hr. Find the speed of the current (c) and the canoe’s speed with no current (s).

8. A plane flew from Shanghai to Singapore a distance of 3000km.

The trip with a head wind took 6 hours. On the return trip with a tail wind the trip took 5 hours. Find the plane’s airspeed (a) and the wind speed (w).

9. Uniforms for the school swim team were sold for $20 for swim suits and $50 for team tracksuits. The total money collected was at most $1000. Write an inequality that describes the situation. Graph the inequality. Give one possible solution to this problem.