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?

• 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.

• 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)

what is the variable that willl be "eliminated"?

5x - 4y = 11

5x + 4y = -14

• x variable

• y variables

• both variables

What would be the first step in finding the solution with elimination?

• cross out the 3y and -3y

• cross out the 4x and x

• change all the signs of the second equation

• add 1 and -11

Solve for y.

(just the number)

Mathematical Equivalence

ON

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)

What is the next step in solving this system by elimination?
2x + 3y = 9
5x + 3y = 21

• Nothing - it is ready to go.

• Multiply one equation by -1

• Multiply the top equation by 3.

• Multiply the bottom equation by 7.

Is this the correct way to multiply the bottom equation by -1?
2x + 3y = 9
-5x - 3y = -21

• Yes

• No