Solving a system of equations x − y = 17, 4 3 x + 3 2 y = 0

Question

Solving a system of equations   x  −  y  =  17,       4    3    x  +      3    2    y  =  0

Jaelynn Cuevas · Accepted Answer

From the first equation by adding to both sides   y you get   x  =  17  +  y. Next try to substitute obtained equation for   x in the second equation.

Kaeden Hoffman · Accepted Answer

Here is an example:                    x        +        y                            =        5                            2        x        +        3        y                            =        10            There are 2 ways I might try to solve this. The first equation tells me that   x  =  5  −  y. The second tells me that   2  x  +  3  y  =  10, so plugging in for   x, I get that   2  (  5  −  y  )  +  3  y  =  10  −  2  y  +  3  y  =  10  +  y  =  10. And thus   y  =  0. Then we also get (from either original equation) that   x  =  5.The other way might be to notice that   x  +  y  =  5 is the same as   2  x  +  2  y  =  10. So then I might subtract   2  x  +  2  y  =  10 from   2  x  +  3  y  =  10 to see that   (  2  x  +  3  y  )  −  (  2  x  +  2  y  )  =  y  =  0  =  (  10  −  10  ). And again,   y  =  0,   x  =  5.Can you apply these methods to this system?

Solving a system of equations x − y = 17 , 4 3 <

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