asiamuhammad6
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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?

Respuesta :

boffeemadrid

Answer:

Step-by-step explanation:

The given equations are:

[tex]2x+3y=15[/tex]                     (1)

and [tex]x-3y=3[/tex]                 (2)

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

[tex]2x+3y+x-3y=15+3[/tex]

[tex]3x=18[/tex]

[tex]x=6[/tex]

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

[tex]6-3y=3[/tex]

[tex]6-3=3y[/tex]

[tex]3=3y[/tex]

[tex]y=1[/tex]

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.

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