Systems Of Linear Equations Worksheets With Answer Key Page 29
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40Exercises
5.4
Help with Homework
1.
WRITING
Describe the difference between the graph of a system of linear
equations that has no solution and the graph of a system of linear equations
that has infi nitely many solutions.
2.
REASONING
When solving a system of linear equations algebraically, how do
you know when the system has no solution? infi nitely many solutions?
Let x and y be two numbers. Find the solution of the puzzle.
3.
4.
1
1
—
—
of x plus 3 is equal to y.
y is
more than 4 times the value of x.
2
3
The difference of 3y and 12x is 1.
x is 6 more than twice the value of y.
Without graphing, determine whether the system of linear equations has
one solution, infi nitely many solutions, or no solution. Explain your reasoning.
5. y = 5x − 9
6. y = 6x + 2
7. y = 8x − 2
y = 5x + 9
y = 3x + 1
y − 8x = −2
Solve the system of linear equations. Check your solution.
π
8. y = 2x − 2
9. y = 3x + 1
10. y =
x + π
—
1
1
3
− π x + 3y = −6 π
y = 2x + 9
− x + 2y = − 3
1
1
11. y = −
x + 5
x + y = 1
13. −2x + y = 1.3
2 2
—
—
12.
6
3
x + 6y = 30
2x + 6y = 6
2(0.5x − y) = 4.6
✗
14.
14.
ERROR ANALYSIS
ERROR ANALYSIS
Describe and correct the
Describe and corr
re
y = −2x + 4
error in solving the system of linear equations.
error in solving the system of linear
y = −2x + 6
The lines have the same slope, so,
there are infi nitely many solutions.
15.
15.
PIG RACE
In a pig race, your pig gets a head start
of 3 feet and is running at a rate of 2 feet per second.
Your friend’s pig is also running at a rate of 2 feet
per second. A system of linear equations that
represents this situation is y = 2x + 3 and y = 2x.
Will your friend’s pig catch up to your pig? Explain.
228
Chapter 5
Systems of Linear Equations
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