Question

Beau has decided to use the method of elimination to solve the system of equations as shown below.

2x+3y=15
x-3y=3

Explain what Beau's first step could be, and why the technique of elimination provides a solution to the system of equations.

3Points
Answer the question using complete sentences and/or mathematical statements. You will earn 1 point for a correct first step and up to 2 points for an appropriate explanation.

HINT: Look at the coefficients of each term. This will help you identify which variable to eliminate.

What should the first step be?
Explain - Why did you identify that step?
How does it help you get closer to a solution?

Answer 1

Explanation:

The given equations are:

`2x+3y=15` (1)

and
`x-3y=3` (2)

Now, simply adding equation (1) and equation (2), we get

`2x+3y+x-3y=15+3`

`3x=18`

`x=6`

Now, substituting the value of x=6 in equation (2). we get

`6-3y=3`

`6-3=3y`

`3=3y`

`y=1`

Thus, the values of x and y are 6 and 1 respectively.

In order to solve the system of solution, beau can see that in both the given equations, coefficient of y is same and is with opposite sign, thus simply adding both the equations will eliminate y and she will get the value of x and then substituting the value of x in any of the equations, she can get the value of y. With this, she can get closer to the solution.