Question

I need HELP!!
what is the solution of the system
6x-9y=25.4
7y-2x=10.5

Answer 1

6x-9y=25.4
7y-2x=10.5

By addition method,
6x - 9y = 25.4
( -2x + 7y = 10.5 ) * 3

gives
6x - 9y = 25.4
-6x + 21y = 31.5

add them.
6x - 9y = 25.4
-6x + 21y = 31.5

= 12y = 56.9
y= 4.74

plug y into one of the original equations to solve for x. x=?


OR......... a different method to solve it....


by substitution method:
6x-9y=25.4 (eq1)
7y-2x=10.5 (eq2)

7y-2x=10.5 (eq2)
solve for y
7y=10.5+2x
y = (2/7)x + (10.5/7)
substitute y into the other equation (the first one, since this y is from the second one)

6x-9y=25.4 (eq1)
6x-9[ (2/7)x + (10.5/7) ]=25.4

solve for x:
6x-[ (2*9/7)x + (10.5*9/7) ]=25.4
6x-[ (2.57)x + (13.5) ]=25.4
6x-(2.57)x - (13.5) =25.4
3.43x = 38.9
x = 11.34
then substitute x into one of the original equations and solve for the y.



but, for grins and giggles, let's check my x and y
6(11.34)-9(4.74)=25.4
6(11.34)-9(4.74)=25.4
68.04 - 42.66 = 25.4
25.38 = 25.4 <-- works, but is off slightly due to rounding.

but if you round the left side, you do get
25.4 = 25.4, so the values for x and y are right.

hope this explains some. This was 2 different methods you could use.