Elimination Steps

What steps can be taken to isolate the y-value?

 $2x-4y=-10$  

 $2x\ +\ 5y\ =17$  

*Hint:  isolating y, means eliminating the x-terms

• Multiply the top equation by -2 and add the result equation to the bottom equation.

• Multiply the bottom equation by -1 and add the result to the top equation.

• Multiply the top equation by 5 and the bottom equation by 4 and adding the two equations.

• Multiplying the top equation by 2 and the bottom equation by 2 and adding the resulting equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

What steps can be taken to isolate the x-terms?

 $4x-y=14$  

 $5x+3y=9$  

**Hint:  isolate the x-term means eliminate the y-terms.

• Multiply the top equation by 3 and add the result to the bottom equation. 

• Multiply the top equation by -3 and add the result to the bottom equation. 

• Multiply the top equation by 5 and the bottom equation by 4 and add the resulting equations.

• Subtract 9 from all terms in the top equation and add the resulting equations.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

If you are solving by elimination and all of the variables cancel leaving the equation "0=0", what does that tell you about the system?

• The lines intersect one time. (one solution)

• The lines are parallel. (no solution)

• The lines coincide. (infinitely many solutions)

• The lines intersect two times. (two solutions)

Tags

CCSS.8.EE.C.8B

A 60 point test is made up of two-point and five-point questions. The test contains 15 questions. If x represents the number of two-point questions and y represents the number of five-point questions, which system models these constraints?

• x + y = 60
  2x + 5y = 60

• 5x + 2y = 15
  2x + 5y = 60

• x + y = 15
  5x + 2y = 60

• x + y = 15
  2x + 5y = 60

Tags

CCSS.8.EE.C.8C

Which of the following are valid steps for isolating the y-term in the system below?

 $-3x\ +\ 4y\ =\ -6$  

 $6x\ -\ 5y\ =\ 3$  

**Hint:  isolating y means to eliminate x.
***Hint:  there are two choices that work, select both!

• Multiply the top equation by 2 and add the result to the bottom equation.

• Multiply the top equation by -5 and the bottom equation by 4 and add the resulting equations.

• Multiply the top equation by 6 and the bottom equation by 3 and add the resulting equation.

• Multiply the top equation by 3 and add the result to the bottom equation.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

If you are solving a system by elimination and all of the variables cancel leaving you with "0 = -9", what does this tell you about the system?

• The lines intersect at (0. -9). (one solution)

• The lines coincide. (infinitely many solutions)

• The lines are parallel. (no solution)

• The lines intersect two times. (two solutions)

Tags

CCSS.8.EE.C.8B

Consider the system:   $3x\ -\ 2y\ =\ 3$  

                                        $-5x\ +\ 9y\ =\ -5$  

Sean mutiplies the top equation by 5 and the bottom equation by 3 to get the system:
 $15x-10y=15$  
 $-15x+27y=-15$  

He adds the two equations together to get  $17y=0$ .
Using inverse operations, he divides both sides by 17 to get  $y=0$  .
What is his next step?

• Substitute 0 in for y in either equation and solve for x.

• He is done, the system has no solution.

• He is done, the system has infinitely many solutions.

• Substitute 0 in for x into one of the equations and solve for y.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6