Have a better way to so a solution check?

Question

3/7x + 5/9y = 27

1/9x + 2/7y = 7
solve by any method:

27x+35y=(97)*27
27x+35y=63*27
27x+35y=1701
27x+35y-35y=1701-35y
27x=-35y+1701
27x/27=(-35y+1701)/27
x=63

27x+35y=2619
(27x+35y)+(-27x)=2619+(-27x)
27x+35y=97*27
y=27(-x+97)/35
y=0

solution check?
there are more than one?

Answer 1

The solution check is simple enough. Just plug in your x-value and y-value into each of the two equations.

For the first equation, you get (3/7)*63 = 27, which is correct.
For the second equation, you get (1/9)*63 = 7, which is correct.
Therefore, your solution is correct.

There's only one solution to this problem. Each equation is a line, and the two lines intersect at exactly one point - that point being (63,0).

Answer 2

There is a simpler way. Your two eqs are

3x/7+5y/9=27...(1)

1x/9+2/?7=7...(2)

Multiply (1) by 1/9 and (2) by 3/7

3x/63+5y/81=3..(3)

3x/63+6y/49=3..(4)
Subtract (4) from (3) and take out y as a common factor

(5/81-6/49)y=0
Since the first factor is NOT zero , y must be zero.
Now put y=o in (1)or (2) and solve for x.

OK?

Answer 3

putting x=63 and y=0 in equation (1)
(3/7)*63+(5/9)*y=27+0=27 checks