There are many ways to check if the point (1,3) is a solution to the linear equation [tex] 5x-9y=32 [/tex].
Let us check it by expressing y in terms of x.
The given expression is 5x-9y=32. If we add -5x to both sides we will get:
[tex] -9y=-5x+32 [/tex]
Multiplying both sides by -1 we will get:
[tex] 9y=5x-32 [/tex]
In order to isolate y, we will divide both sides by 9 to get:
[tex] y=\frac{5}{9}x-\frac{32}{9} [/tex]
Now let us plug in the given value of x=1 from the point (1,3). This should give us y=3. Let us see if we get y=3 when we plug x=1 in the above equation.
[tex] y=\frac{5}{9}\times 1-\frac{32}{9}=\frac{5-32}{9} [/tex]
[tex] \therefore y=\frac{-27}{9}=-3 [/tex]
Thus, we see that when x=1, y=-3 and that [tex] y\neq 3 [/tex] and hence we conclude that the point (1,3) is not a solution to the original given linear equation 5x-9y=32.
For a better understanding of the explanation given here a graph has been attached. As can be seen from the graph, (1,3) does not lie on the straight line that represents 5x-9y=32, but (1,-3) does lie on it as we had just found out.
