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.

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.

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)

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

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.

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)

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.