Solving Systems by SUBSTITUTION

What is the 1st step of the SUBSTITUTION method?

• Rewrite both equations so that they are in slope-intercept form

• Write final answer as an ordered pair (x, y)

• Look for/create a set of opposites with x or y

• Solve one of the equations for one of its variables (Get one variable by itself x = or y =)

Is there an equation solved for one of the variables?

 $x\ =4y\ +\ 7$  

 $6x\ +\ 2y\ =\ 68$  

• YES, there is one equation that is written as:  x = or y =

• NO, we would need to solve for x or y in one of the equations

Which is the correct substitution of the following system:

 $x\ =4y\ +\ 7$  

 $6x\ +\ 2y\ =\ 68$  
(2nd step of the substitution method)

•  $6x\ +\ 2\left(4y\ +\ 7\right)\ =\ 68$  

•  $6\left(4y\ +\ 7\right)\ +\ 2y\ =\ 68$  

•  $6x\ +\ 2y\ =\ \left(4y\ +\ 7\right)$  

•  $\left(4y\ +\ 7\right)\ =\ 68$  

Solve the system using the SUBSTITUTION method

 $x\ =4y\ +\ 7$  

 $6x\ +\ 2y\ =\ 68$  

•  $\left(1,\ 11\right)$  

•  $\left(11,\ 1\right)$  

•  $\left(4,\ 23\right)$  

•  $\left(23,\ 4\right)$  

Is there an equation solved for one of the variables?

 $x\ +\ 2y\ =\ 10$  

 $x\ +\ y\ =\ 6$  

• YES, there is one equation that is written as:  x = or y =

• NO, we would need to solve for x or y in one of the equations

Solve the 2nd equation for y (get the y by itself).

 $x\ +\ 2y\ =\ 10$  

 $x\ +\ y\ =\ 6$  

•  $y\ =\ -x\ +\ 6$  
  

•  $y\ =\ x\ +\ 6$  
  

•  $y\ =\ -x\ -\ 6$  

•  $y\ =\ x\ -\ 6$  

Solve the system using the answer to the previous question (x = 2).
 $x\ +\ 2y\ =\ 10$ 
 $x\ +\ y\ =\ 6$  

•  $\left(2,\ 4\right)$ 
  

•  $\left(2,\ -4\right)$  
  

•  $\left(4,\ 2\right)$  

•  $\left(-4,\ 2\right)$  

Solve the system using the SUBSTITUTION method

 $x\ -\ 8y\ =19$ 
 $7x\ +\ 6y\ =\ 9$  

• (35, -2)

• (-2, 35)

• (-2, 3)

• (3, -2)