6x - 2y = 4; (1,1) (2,4)
Show that the two ordered pairs are solutions to the given equation.
When I solved the soultions were 4, please help.
The solutions were 4 what?
$\displaystyle 6x - 2y = 4$
Let's try (1, 1) first.
$\displaystyle 6(1) - 2(1) = 4$
$\displaystyle 6 - 2 = 4$
$\displaystyle 4 = 4$ Check!
You put in the (2, 4) point. If the left hand side comes out to be 4 then the point satisfies the equation.
-Dan
By solve the equation it means rewrite the equation so that y is by itself on one side of the equal sign and everything else is on the other side. Do that first, then plug in your ordered pairs (x,y).
$\displaystyle 6x - 2y = 4$ this is what you are given
$\displaystyle -2y = 4-6x$ subtract $\displaystyle 6x$ from both sides
$\displaystyle y = 3x-2$ divide both sides by $\displaystyle -2$.
For the second ordered pair (2,4) plug the x-value (2) wherever you see x and see if you get the y-value (4).
$\displaystyle y = 3x-2 = 3(2)-2 = 6-2 = 4$.
To shown an ordered pair is a solution we need to evaluate and see if you get a true statement.
for the first one x=1 and y=1 so
$\displaystyle 6(1)-2(1) \underbrace{=}_{\mbox{is this true}}4$ So we simplify and see
$\displaystyle 4=4$ so yes it is a solution.
For the next one x=2 y=4
$\displaystyle 6(2)-2(4) \underbrace{=}_{\mbox{is this true}}4$ So we simplify and see
$\displaystyle 4=4$ so this is also a solution.
I hope this clears it up.
Good luck
B
Armygirl,
You are essentially checking to see if a point lies on a line equation.
Go here:
Determine if a point lies on a line
Try both points and it will show you the math work how to solve these proving that both points lie on the line.
Edit: I just saw i knowone's post just now.