6-1 Graphing Systems of Equations
Graph each system and determine the number of solutions that it has. If it has one solution, name it.
30. 8x − 4y = 16
−5x − 5y = 5
ANSWER: 1 solution, (1, –2)
31. 3x + 5y = 30
3x + y = 18
ANSWER: 1 solution, (5, 3)
32. −3x + 4y = 24
4x − y = 7
ANSWER: 1 solution, (4, 9)
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33. 2x − 8y = 6
x − 4y = 3
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6-1 Graphing Systems of Equations
32. −3x + 4y = 24
4x − y = 7
ANSWER: 1 solution, (4, 9)
33. 2x − 8y = 6
x − 4y = 3
ANSWER: infinitely many
34. 4x − 6y = 12
−2x + 3y = −6
ANSWER: infinitely many
35. 2x + 3y = 10
4x +Manual
6y = 12
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ANSWER: no solution
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6-1 Graphing Systems of Equations
35. 2x + 3y = 10
4x + 6y = 12
ANSWER: no solution
48. CHALLENGE Use graphing to find the solution of the system of equations 2x + 3y = 5, 3x + 4y = 6, and 4x + 5y =
7.
ANSWER: (−2, 3)
49. CCSS ARGUMENTS Determine whether a system of two linear equations with (0, 0) and (2, 2) as solutions
sometimes, always, or never has other solutions. Explain.
ANSWER: Always; if the equations are linear and have more than one common solution, they must be consistent and dependent,
which means that they have an infinite number of solutions in common.
50. WHICH ONE DOESN’T BELONG? Which one of the following systems of equations doesn’t belong with the
other three? Explain your reasoning.
ANSWER: Sample answer: 4x + 2y = 14, 12x + 6y = 18; This system is inconsistent while the others are consistent and
independent.
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sometimes, always, or never has other solutions. Explain.
ANSWER: Always; if Systems
the equations
are linear and have more than one common solution, they must be consistent and dependent,
6-1 Graphing
of Equations
which means that they have an infinite number of solutions in common.
50. WHICH ONE DOESN’T BELONG? Which one of the following systems of equations doesn’t belong with the
other three? Explain your reasoning.
ANSWER: Sample answer: 4x + 2y = 14, 12x + 6y = 18; This system is inconsistent while the others are consistent and
independent.
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