# solving systems of equations in two variables

**Question description**

Estimate the solution of the system of equations shown in the graph below?

o (1, 0) and (-3, 0)

o (0, -3) and (0, -1)

o (-1, -2)

o (-2, -1)

If a system of equations has exactly one solution, it is ____________________?

o consistent and independent

o inconsistent and independent

o inconsistent and dependent

o consistent and dependent

Which of the following graphs best represents a system of equations that has no solution?

o

o

o

o

A student uses the substitution method to solve the system of equations below algebraically.

2x - y = 5

3x + 2y = -3

Which equation could be used?

o 3x + 2(2x - 5) = -3

o 3x + 2(5 - 2x) = -3

o 3(y + 5/2) + 2y = -3

o 3(5/2 - y) + 2y = -3

Which linear system has been correctly solved for one of the variables from the following system?

2x - y = -1

2x + y = -7

o 2x - y = -1

y = 2x - 7

o 2x - y = -1

y= -2x +7

o y = 2x + 1

2x + y = -7

o y = -2x + 7

2x + y = -7

Which linear system has the solution (6, 6)?

o 3 x + y = 4

4 x - 3 y = 1

o 4 x + 3 y = 0

2 x - y = 0

o 4 x - 3 y = -1

-2 x + y = -3

o x + y = 12

3x - 2y = 6

A student is using the elimination method to solve the system of equations below. What is the best first step?

3x - y = 5

2x + 3y = 10

o Multiply the first equation by 2.

o Multiply the second equation by 3.

o Multiply the first equation by 3.

o Multiply the second equation by 2.

In which line is a mistake first made when solving the following system of equations by elimination for s?

2r + 7s = 11

r - 9s = -7

Line 1 | 2r + 7s = 11 2(r - 9s = -7) |

Line 2 | 2r + 7s = 11 2r - 18s = -14 |

Line 3 | -11s = -3 |

Line 4 | s = 11/3 |

o Line 1

o Line 2

o Line 3

o Line 4

Find the solution to the system of equations.

4c = 3d + 3

c = d - 1

o c = 6, d = 7

o c = 3, d = 4

o c = 8, d = 7

o c = 5, d = 4

What is the solution to the system of equations.

2x - 3y = -9

-x + 3y = 6

o (3, 3)

o (-3, 1)

o (-3, 3)

o (1, -3)

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