Question

3. To combine the equations and solve for one of the variables, you need to eliminate the other variable. How can you change one equation so that one variable is eliminated when the two equations are added? Explain and write the new equation. (12x + 6y = 120 and 4x + y = 30)

Answer 1

Answer: 12x + 6y= 120 and -24x -6y = -180

Explanation:

12x + 6y = 120

4x + y = 30

To eliminate one of the variables the coefficients have to have the same values but different signs.One has to be positive and one has to be negative then you could add them up to get become zero. So in the two systems of equations you can multiply the down equation by -6 to eliminate the y variable but the top equation will have to be the same.

-6(4x + y)=30(-6)

-24x -6y = -180

You can now rewrite the equation as

12x + 6y = 120

-24x -6y = -180 Now you can add the top and down equations to eliminate the y variable.

Answer 2

You can multiply the 2nd equation by either -3 or -6

Explanation:

If you are using elimination (imo substitution on this problem would be easier), then you need to eliminate one of the variables. If you are wanting to eliminate x first, then multiply by -3. If you want to eliminate y first, then multiply by -6.