Answer to Question #350905 in Algebra for bogart

Question

Find the solution set of the following using 3 methods. Show your solutions, then submit your answer to your eLMS dropbox.

1. 2x + y = 15

    x - y = 9

 

Answer 1

Solution:

There are three methods of solving leaner systems of equations: substitution, elimination and graphing.

Let's first substitution method:

$2x+y=15;\space x-y=9;$ from second equation:

$y=x-9;$ Now we will substitute $y$ in first equation:

$2x+x-9=15; \space$

$3x=15+9=24;$

$x=\frac{24}{3}=8;$ So,

$y=x-9=8-9=-1;$

Second elimination method:

When we use elimination to solve a system, it means that we’re going to get rid of (eliminate) one of the variables. So we need to be able to add the equations, or subtract one from the other, and in doing so cancel either the x-terms or the y-terms.

We need to just add both equations left to left and right to right sides;

$(2x+y)+(x-y)=15+9;$

$3x=24; \space x=8;$

$y=x-9=8-9=-1;$

Third method graphing: In order to graph these equations, let’s put both of them into slope-intercept form. We get:

$y=15-2x;$

$y=x-9;$

Now drawing their graphs (I can not drop .jpg version of the drawn graph, I drop it, but I do not see here), we can see the coordinate intersection point's of the equations (8; -1).

So, solution: $x=8;\space y=-1;$

Answer:

$x=8;\space y=-1.$