How do you solve the simultaneous equations #3r - 2t = -0.2# and #r + s = 2.4#?

1 Answer
Aug 26, 2015

Answer:

You can not solve for the values of 3 variables with only 2 equations;
however, if the second equation was meant to be #r+t=2.4# then
#(r,t)=(0.92,1.48)#

Explanation:

The best we could do with 2 equations with 3 unknowns is generate a linear relationship between two of the variables:
For example, by solving for #r#
#3r-2t = -0.2color(white)("XXXXXX")rarrcolor(white)("XX")r=(2t-0.2)/3#
and
#r+s= 2.4color(white)("XXXXXXXXX")rarrcolor(white)("XX")r= 2.4-s#

So
#color(white)("XX")(2t-0.2)/3 =2.4-scolor(white)("XX")rarrcolor(white)("XX")2t-7.2s = 0.2#

If however the equations were meant to be (in only two variables):
[1]#color(white)("XX")3r-2t= -0.2#
[2]#color(white)("XX")r+t= 2.4#

Multiplying [2] by 2:
[3]#color(white)("XX")2r+2t=4.8#

Adding [1] and [3]
[4]#color(white)("XX")5r= 4.6#

Dividing by 5
[5]#color(white)("XX")r=0.92#

Substituting #0.92# for #r# in [2]
[6]#color(white)("XX")0.92+t=2.4#

Subtracting #0.92# from both sides
[7]#color(white)("XX")t = 1.48#