Solving pairs of linear equations in two variables

In a system of linear equations, if the lines are parallel and have the same y-intercept, how many solutions does the system have?

• Two solutions

• One solution

• Infinite solutions

• No solution

You are solving a system of equations and you get

4=7.

What is the solution?

• Infinitely many solution (IMS)

• (0, 0)

• No solution (NS)

• (4, 7)

• The x variable would be easiest to eliminate

• The y variable would be easiest to eliminate

• We would multiply top equation by 2

• Would multiply the bottom equation by 2

• This system has no solution

The pair of equations x=0 and x=5 has...

• no solution

• unique / one solution

• two solutions

• infinitely many solutions

The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if

• (a) a = b

• (b) 3a = 2b

• (c) 2a = 3b

• (d) ab = 6

If I solve a system of equations, and the answer at the end is 0=2, what is the solution?

• 2

• Infinite solutions

• 0

• No solution

Solve by elimination:

3x+7y=23

-3x-7y=-17

• No solution

• Infinite number of solutions

• (-3,3)

• (3,3)

When solving a system algebraically, which expression indicates there is no solution?

*Select all that apply*

•  $x=0$  

•  $0=1$  

•  $-2=-2$  

•  $y=7$  

•  $-6=1$  

Which system has no solution?

• y = 7x - 2

  -7x + y = 4

• y = 2x - 1

  y = x + 1

• -6x + 2y = 12

  y = 3x + 6

If you were using the substitution method and found "x=0". This means there is no solution.

• True

• False