This is a System of Equations, so basically what we want to do is to get one of these variables to equal zero. However none of the variables are equal, 7x doesn't equal 3x and 3y is not 7y. So we need to multiply both equations in the system to make one of these variables equal.
Let's Multiply The Top One By 3
[tex]3x - 7y = 6 \\ 3(3x - 7y) = 3(6) \\ 9x - 21y = 18[/tex]
Let's Multiply The Bottom One By 7
[tex]7x + 3y = 72 \\ 7(7x + 3y) = 7(72) \\ 49x + 21y = 504[/tex]
Now As You Can See 21y and -21y are equal, aand by that I mean that they will equal zero once added.
Now We Solve The System
1st. Add Straight Down Ex. 9x+49x, -21y+21y, 18+504
[tex]9x - 21y = 18\\ 49x + 21y = 504 [/tex]
Add Straight Down
[tex]58x + 0y = 522 \\ 58x + 0 \times y = 522 \\ 58x = 522[/tex]
Now we Solve For X
[tex]58x = 522 \\ \frac{58x}{58} = \frac{522}{58} \\ x = 9[/tex]
Now We've Found X, We Need Y, and We Can Find It By Plugging In X To One of The ORIGINAL EQUATIONS.
One Of The Original Equations
[tex]3x - 7y = 6[/tex]
1st. X=9, So Replace X with 9
[tex]3(9) - 7y = 6 \\ 27 - 7y = 6 [/tex]
Solve For Y
[tex] - 7y = 6 - 27 \\ - 7y = - 21 \\ \frac{ - 7y}{ - 7} = \frac{ - 21}{ - 7} \\ y = 3[/tex]
Now We Test It, X=9, Y=3
[tex]3x - 7y = 6 \\ 3(9) - 7(3) = 6 \\ 27 - 21 = 6 \\ 6 = 6[/tex]
AND
[tex]7x + 3y = 72 \\ 7(9) + 3(3) = 72 \\ 63 + 9 = 72 \\ 72 = 72[/tex]
SO: ANSWER
[tex]x = 9 \\ y = 3[/tex]
