Algebra II Honors
WS Solving Systems of Linear Equations
Solve each system by graphing.
3𝑥 − 𝑦 = 8
1. {
10 + 𝑠𝑦 = 4𝑥
2. {
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𝑦 + 5 = 2𝑥
3𝑦 + 6𝑥 = −3
Classify each system as independent, dependent, or inconsistent.
3𝑦 + 2𝑥 = 12
−2𝑦 = 20 − 2𝑥
15𝑥 = 10𝑦 − 20
3. {
4. {
5. {
36 − 9𝑦 = −6
3𝑦 − 6𝑥 = −30
18 + 9𝑥 = 6𝑦
Solve by substitution.
5𝑚 − 𝑛 = 7
6. {
3 + 3𝑛 = 6𝑚
7. {
Solve by elimination.
5𝑥 − 4𝑦 = 8
9. {
14 + 4𝑦 = 3𝑥
8𝑦 + 10 = 6𝑥
10. {
8𝑦 − 4𝑥 = −12
4𝑦 − 6 = 2𝑥
𝑦 − 3𝑥 = 9
3𝑢 + 8 = 4𝑣
8. {
24𝑣 = 6 − 3𝑢
11 − 2𝑐 = 3𝑑
11. {
2𝑐 − 7𝑑 = −9
Write a system of equations and solve.
12. The sum of the digits of a two digit number is 12. If the digits are reversed, the new number
is 18 less than the original number. Find the original number.
13. The sum of the digits of a two digit number is 14. If the number represented by reversing
the digits is subtracted from the original number, the result is 18. What is the original
number?
14. Against the head wind, Jeff computes his flight time for a trip of 2900 miles at 5 hours. The
flight would take 4 hours and 50 minutes if the head wind were half as much. Find the head
wind and the plane’s air speed.
15. A motorboat took 3 hours to make a downstream trip with a current of 6 km/h. The return
trip against the same current took 5 hours. Find the speed of the boat in still water.
16. A train leaves Slaton traveling east at 80 km/h. An hour later, another train leaves Slaton on
a parallel track at 120 km/h. How far from Slaton will the two trains meet?
17. The sum of 3 numbers is 6. The difference of the first two numbers, plus the third number
equals 2. The sum of the first two numbers, minus the third, equals 0. Find the numbers.