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. (3 points: 2 for your explanation and
1 for the equation)

Answer 1

If we multiply equation 2 with -6 and add both equations, we can eliminate variable y. The equation is given and solved below.

Explanation:

The equations given are:

12x+6y=120

4x+y=30

We need to find How can you change one equation so that one variable is eliminated when the two equations are added?

Let:

`12x+6y=120--eq(1)\\4x+y=30--eq(2)`

If we multiply equation 2 with -6 and add both equations, we can eliminate variable y.

Solving

`12x+6y=120\\-24x-6y=-180\\---------\\-12x+0y=-60\\-12x=-60\\x=(-60)/(-12)\\x=5`

So, we eliminated the variable y and found the value of x.

Now Putting value of x in any of above equations we can find value of y.

`4x+y=30\\4(5)+y=30\\y=30-20\\y=10`

So, we get value of y=10