Solve Systems of Linear Equations and Inequalities

Solve Systems of Linear Equations & Inequalities

Questions answered:

• How do I write and graph linear equations?

• How do I Solve a System of Linear Equations by Graphing?

• How do I Solve a System of Linear Equations by Substitution?

• How do I Graph a Linear Inequality?

• How do I Solve a System of Linear Inequalities?

How do I write and graph linear equations?

Multiple Choice

Write the following equation in slope-intercept form:

 $4x-y=3$  

•  $y=4x+3$  

•  $y=-4x-3$  

•  $y=-4x+3$  

•  $y=4x-3$  

• None of the above

Multiple Choice

Which graph shows the solution set of:

 $y=-x+5$  

Multiple Choice

Which graph shows the solution set of:

 $-3x=-9$  

How do I Solve a System of Linear Equations by Graphing?

Multiple Select

What are the different possible solutions to a system of linear equations?

• No Solution

• One Solution

• Two Solutions

• Infinitely Many Solutions

• Conditional Solution

Multiple Select

Which of the following have infinitely many solutions?

Multiple Choice

Which graph shows the solution to:

 $y=-3x+5$     &     $y=\frac{2}{3}x-6$  

How do I Solve a System of Linear Equations by Substitution?

Multiple Choice

Which answer shows the correct substitution step for:

 $3y-2x=5$  
 $x=4y-7$  

•  $3\left(4x-7\right)-2x=5$  
  

•  $3\left(4y-7\right)-2x=5$  
  

•  $3y-2\left(4y-7\right)=5$  
  

•  $x=4\left(3y-2x\right)-7$  
  

•  $3y-2x=4y-7$  

Multiple Choice

TJ solves the following system by substitution. He gets the answer x=9. What error did he make?

• Substituted incorrectly in Step 1.

• Simplified incorrectly (Step 1 to Step 2).

• Step 3 should be:  $x=-1$  

• Substituted x=9 into the wrong equation.

• TJ solved correctly.

Multiple Choice

Solve using substitution:

 $y=-2x+5$  
 $y=3x$  

•  $\left(5,15\right)$  
  

•  $\left(-1,3\right)$  
  

•  $\left(1,3\right)$  
  

•  $\left(3,1\right)$  
  

•  $\left(-5,-15\right)$  

How do I Graph a Linear Inequality?

Multiple Choice

Write the inequality for the graph:

• 
  

  $y>2x+1$
  

• $y<2x+1$

• $y\ge2x+1$

• $y\le2x+1$

• $y>x+2$

Multiple Choice

Select the correct graph for each inequality.

• A

• B

• C

• D

Multiple Choice

Select the correct graph for each inequality.

• A

• B

• C

• D

• None of the above

How do I Solve a System of Linear Inequalities?

Multiple Choice

Which answer best describes the solution set to a system of inequalities?

• Every point in the blue OR the red region.

• Every point in the OVERLAPPING red/blue region.

• Every point in the BLUE region

• Every point in the RED region

• ONLY the points on the lines.

Multiple Select

The system of inequalities is:

y ≤ -x

y < 2x + 3

What are the solutions (select all that apply)?

• (-1, 0)

• (0, 1)

• (-1, 2)

• (0, -2)

• (-1, -1)

Multiple Choice

What graph represents the inequalities?

Multiple Choice

Which system of inequalities matches the graph?

• y > 2x - 4

  y < 2

• y < 2x - 4

  y < 2

• y > 2x - 4

  y < 2

• y < 2x - 4

  y < -2