Resolve 120 x + y + 60 x − y = 6 ; 80 x + y + 100 x − y = 7I want to resolve this system of equations: { 120 x + y + 60 x − y = 6 80 x + y + 100 x − y = 7 I came to equations like x − 10 x x − y + y − 10 y x − y = 20and − 2 x y − y 2 − 10 y = 20 − x 2 − 10 xI need to leave x or y alone and didn't succeed. Any help?

Question

Resolve       120          x      +      y        +      60          x      −      y        =  6  ;        80          x      +      y        +      100          x      −      y        =  7I want to resolve this system of equations:      {                                        120                          x              +              y                                +                      60                          x              −              y                                =          6                                                  80                          x              +              y                                +                      100                          x              −              y                                =          7                        I came to equations like  x  −            10      x              x      −      y        +  y  −            10      y              x      −      y        =  20and  −  2  x  y  −      y    2    −  10  y  =  20  −      x    2    −  10  xI need to leave x or y alone and didn&#039;t succeed. Any help?

Danube2w · Accepted Answer

You could also solve by eliminating one of the variables:Multiply the first equation by 100 and the second by 60:      12000          x      +      y        +      6000          x      −      y        =  600      4800          x      +      y        +      6000          x      −      y        =  420Subtract them from each other and get rid of       6000          x      −      y        x  +  y  =      720    180    =  40Substitute   x  +  y into either of your original equations:      120          x      +      y        +      60          x      −      y        =  6    ⟹        120    40    +      60          x      −      y        =  6  x  −  y  =  20Now solve these two simultaneous equations:  x  +  y  =  40  ,     x  −  y  =  20Now solve these two simultaneous equations:  x  +  y  =  40  ,     x  −  y  =  20Trust you can finish this off

Isaiah Owens · Accepted Answer

Let   u  =      1          x      +      y       and   v  =      1          x      −      y      . Solve first for   u  ,  v, then you&#039;ll get equations   x  +  y  =      1    u   and   x  −  y  =      1    v   to solve for   x  ,  y(It&#039;s slightly easier to use   u  =      20          x      +      y       and   v  =      20          x      −      y       and then solve   x  +  y  =      20    u   and   x  −  y  =      20    v  .)

Resolve 120 x + y </mrow> </mfrac> + 60

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