In these equations what do x and y equal?

  -5x-7=8y      →  -5x - 8y = 7        (1)

   3y=-2x-9    →    2x + 3y  = -9     (2)

Multiply  (1)  by 3   and  (2)  by 8   and we have

-15x - 24y   =   21

16x + 24y   =  -72        add these

  x              =   -51

And using any equation - I'll use (2)  - we can find y

2(-51)  +  3y   = -9

-102 + 3y  = -9      add 102 to both sides

3y  =  93     divide both sides by 3

y =  31

1-

Solve the following system: {-7-5 x = 8 y | (equation 1) 3 y = -9-2 x | (equation 2) Express the system in standard form: {-(5 x)-8 y = 7 | (equation 1) 2 x+3 y = -9 | (equation 2) Add 2/5 × (equation 1) to equation 2: {-(5 x)-8 y = 7 | (equation 1) 0 x-y/5 = (-31)/5 | (equation 2) Multiply equation 2 by -5: {-(5 x)-8 y = 7 | (equation 1) 0 x+y = 31 | (equation 2) Add 8 × (equation 2) to equation 1: {-(5 x)+0 y = 255 | (equation 1) 0 x+y = 31 | (equation 2) Divide equation 1 by -5: {x+0 y = -51 | (equation 1) 0 x+y = 31 | (equation 2) Collect results: Answer: | | {x = -51              y = 31

2-

Solve the following system: {2 x-3 y = 7 | (equation 1) x = 4 y-11 | (equation 2) Express the system in standard form: {2 x-3 y = 7 | (equation 1) x-4 y = -11 | (equation 2) Subtract 1/2 × (equation 1) from equation 2: {2 x-3 y = 7 | (equation 1) 0 x-(5 y)/2 = (-29)/2 | (equation 2) Multiply equation 2 by -2: {2 x-3 y = 7 | (equation 1) 0 x+5 y = 29 | (equation 2) Divide equation 2 by 5: {2 x-3 y = 7 | (equation 1) 0 x+y = 29/5 | (equation 2) Add 3 × (equation 2) to equation 1: {2 x+0 y = 122/5 | (equation 1) 0 x+y = 29/5 | (equation 2) Divide equation 1 by 2: {x+0 y = 61/5 | (equation 1) 0 x+y = 29/5 | (equation 2) Collect results: Answer: | | {x = 61/5           y = 29/5

Example 2    x=4y-11    substitute this 'x' into the first equation

             2x-3y=7

             2(4y-11) -3y=7

            8y -22 - 3y =7

            5y = 7+22

             y= 29/5       Then   since x=4y-11   x=  4 (29/5) -11= 116/5 -55/5= 61/5