SOAR Alg1 | 6-1 Systems of Equations: Number of Solutions

Multiple Choice

What is a system of linear equations?

• A single linear equation with multiple variables.
• A pair of equations that includes both linear and quadratic equations.

• A pair of linear equations with the same variables.

• A collection of nonlinear equations with the same variables.

Multiple Choice

Which of these is a system of linear equations?

• $$y=2x+3$$

  $$y=-x+1$$

• $$y=x^2+4$$

  $$y=3x+5$$

• $$y=-5x-2$$

  $$a=9b+4$$

• $$y=\frac{1}{2}x-3$$

Match

Match the correct number of solutions with each graph.

1 solution

No solution

Infinitely many solutions

• 1 solution

• No solution

• Infinitely many solutions

Graphing

Graph the line:

$$y=x+1$$

Graphing

Graph the line:

$$y=x+7$$

Multiple Choice

Here is a graph of the system:

$$y=x+1$$ and $$y=x+7$$

How many solutions does the system of equations have?

• No solution

• 1 solution

• Infinitely many solutions

Graphing

Graph the line:

$$y=x-2$$

Graphing

Graph the line:

$$y=-\frac{3}{2}x-7$$

Multiple Choice

Here is a graph of the system:

$$y=x-2$$ and $$y=-\frac{3}{2}x-7$$

How many solutions does the system of equations have?

• No solution

• 1 solution

• Infinitely many solutions

Multiple Choice

Is (4,10) a solution to this system of equations?

$$y=x+6$$

$$y=2x+2$$

• YES

• NO

Multiple Choice

Is (1,1) a solution to this system of equations?

$$6x+14y=20$$

$$8x+y=6$$

• YES

• NO