Substitution Practice Step By Step

Substitution Practice Step By Step

Write this problem on paper or a whiteboard

• We will go through each individual step in the following questions all together

Multiple Choice

Step 1: Rewrite one of the equations that has a variable with no number in front of it as x= or y=

• $y=-3x-1$

• $y=3x-1$

• $y=\frac{4}{3}x+\frac{5}{4}$

• $x=\frac{1}{3}y+\frac{1}{3}$

Multiple Choice

Step 2: Substitute the right half of the equation you just found in place of that variable of the other equation  $\left(y=3x-1\right)$  

•  $6x-8y\left(3x-1\right)=-10$  

•  $6\left(3x-1\right)-8y=-10$  

•  $6x-8\left(3x-1\right)=-10$  

•  $6x-8\left(3x-1\right)$  

Multiple Choice

 $6x-8\left(3x-1\right)=-10$  Step 3: Distribute

•  $6x-24x+8=-10$  

•  $-6x+2=-10$  

•  $6x-24+8=-10$  

•  $6x+24x-8=-10$  

Multiple Choice

 $6x-24x+8=-10$  

Step 4: Combine Like Terms

•  $30x=-18$  

•  $18x+8=-10$  

•  $-30x=-2$  

•  $-18x+8=-10$  

Multiple Choice

 $-18x+8=-10$  

Step 5: Solve for x

•  $-18x=-18,\ x=1$  

•  $-18x=-18,\ x=-1$  

•  $-18x=-2,\ x=\frac{2}{18}$  

•  $-18x==18,\ x=0$  

Multiple Choice

Step 6: Plug your answer back into an original equation. Any equation is correct, but one is the easiest. Choose the easiest here. x=1

•  $6\left(1\right)-8y=-10,\ y=2$  

•  $-3\left(1\right)+y=-1,\ y=2$  

•  $y=3\left(1\right)-1,\ y=2$  

•  $y=3x\left(1\right)-1,\ y=2x$  

Poll

How did you feel about that?

• Great!

• It helped me figure out the steps

• I don't get it

• Please help me!

• Oh look a squirrel!

Write down this problem on whiteboard/paper

We are going to do it step by step together again. Write down each step on your paper as we go. Correct any of the mistakes you make.

Multiple Choice

Step 1: Rewrite one of the equations that has a variable with no number in front of it as x= or y=

• $y=-\frac{1}{4}x-\frac{11}{4}$

• $y=\frac{6}{7}x+\frac{4}{7}$

• $x=4y-11$

• $x=-4y-11$

Multiple Choice

 $x=-4y-11$  

Step 2: Substitute the right half of the equation you just found in place of that variable of the other equation 

•  $-6\left(-4y-11\right)+7y=4$  

•  $-6x+7\left(-4y-11\right)=4$  

•  $-6x\left(-4y-11\right)+7y=4$  

•  $-6\left(-4y-11\right)=4$  

Multiple Choice

 $-6\left(-4y-11\right)+7y=4$  

Step 3: Distribute

•  $24y+66+7y=4$  

•  $-24y-66+7y=4$  

•  $-10y-17+7y=4$  

•  $-4y-66+7y=4$  

Multiple Choice

 $24y+66+7y=4$  

Step 4: Combine Like Terms

•  $17x+66=4$ 

•  $31y=70$  
  

•  $31y=62$  

•  $31y+66=4$  

Multiple Choice

 $31y+66=4$  

Step 5: Solve for y

•  $31y=-62,\ y=-2$  

•  $31y=-62,\ y=2$  

•  $31y=-62,\ y=-\frac{1}{2}$  

•  $31y=-70.\ y=\frac{-70}{31}$  

Multiple Choice

Step 6: Plug your answer back into an original equation. Any equation is correct, but one is the easiest. Choose the easiest here. y=-2

• $-6x+7\left(-2\right)=4,\ x=-3$

• $x+4\left(-2\right)=-11,\ x=-3$

• $x=-4\left(-2\right)-11,\ y=-3$

•  $x=-4y\left(-2\right)-11,\ x=-3y$  

Poll

How did you feel about that?

• We good

• It helped me figure out the steps

• I don't get it

• Please help me!

• Is ice a rock?