Substitution

Which image shows a system of linear equations with infinitely many solutions?

• 
• 
• 
• 

What is the solution to this system of equations?

• (4, -1)
• (-1, 4)
• (-4, 1)
• (-4, -1)

Buzz graphed two lines in order to find the solution to a given system of equations.
What is the solution?

• (-1, 4)
• (1, -4)
• (-4, 1)
• (4, -1)

What is the first step in solving a system by Substitution?

• Make sure both equations are in standard form.
• Make sure at least one equation is solved for one variable.
• Make sure both equations are in slope-intercept form.
• Make sure both equations can be solved.

If a system of equations has no solution, what does the graph look like? 

• intersecting lines
• parallel lines
• skew lines
• intersecting lines

Which answer has a correct first step for this system:

3x + 3y = 3

y = 3x + 5

• The variable is already isolated, so we've already solved the system.

• The variable is already isolated for y, so we substitute it in the first equation and solve for x

  3x + 3(3x + 5) = 3

• Free sha vaca doo

• The variable is already isolated for y, so we substitute it in the second equation and solve for x

  y = 3(3x + 3y) = 3

• 2x + 6(-5x) = -3

• 2x - 5x = -3

• y + 6(-5y) =-3

• 2(-5x) + 6y = -3

To solve this system by substitution:

2x+2y=10

y=5+x

Your first step would be...

• 2x+2(5+x)=10

• 2x+2y+5+x=10

• y=5+x+2x+2y

• 10=5+x

2x+y=3

x=3y+5

The next step in substitution would be...

• 2x+3y+5=3

• 2(3y+5)+y=3

• 2x+x=3

• 3y+5=3

x+y=3

2x+4y=8

Your next step would be...

• Isolate x or y in x+y=3

• 2x+x=3

• x+2x+4y=8

• 2x+x=8