Three variable equations

Question

8r-s+t=-1

 

2r+2s-3t=-22

 

r-3s+2t=14

Answer 1

8r-s+t=-1                                  Eq. 1

2r+2s-3t=-22                             Eq. 2

r-3s+2t=14                                Eq. 3

 

t = -8r + s - 1                            Solve Eq. 1 for t.

 

Substitute the value of t into Eq. 2.

 

2r 2s-3(-8r+s-1)= -22

2r+2s+24r-3s+3= -22

26r-s= -25

 

Substitute the value of t into Eq. 3.

r-3s+2(-8r+s-1)= 14

r-3s-16r+2s-2= 14

-15r-s= 16

 

Subtract Eq. 3 from Eq 2.

 

    26r-s= -25 -

  (-15r-s= 16)

    41r= -41                This implies that r= -1.

 

26r-s= -25                  Solve Eq. 2 for s by substituting the value of r.

26(-1)-s= -25

       s= -1

 

t = -8r + s - 1                 Solve Eq. 1 for t by substituting the values of r and s.

t = -8(-1) + (-1) -1

t = 8-1-1 = 6.

 

Check by substituting the values of r, s, and t into the original equations.

Eq. 1

8r-s+t=-1

8(-1)-(-1)+(6)=-1

-8+1+6=-1

-8+7=-1

-1=-1                  Checks!

 

 

 

2r+2s-3t=-22

2(-1)+2(-1) -3(6)= -22

-2-2-18=-22

-22=-22              Checks!

 

 

r-3s+2t=14

-1-3(-1)+2(6)= 14

-1+3+12= 14

-1+15=14

14=14                 Checks!