Question 128663
{{{2x+(1/5)y=6}}}


Look at your equation as a rule for describing a set of points that lie in a straight line -- hence the term, 'linear' equation.  By writing the equation, you have created a relationship between the equation and that set of points such that if you substitute the x- and y-coordinate values from any point that IS on the line back into the equation, you will get a true statement.  On the other hand, if you substitute the x- and y-coordinates from a point that IS NOT on the line, you will get a false statement.


Let's use a simple example to illustrate the concept.  We'll use {{{y=2x}}}.  The point (1,2) lies on the line, and we know this for sure because if we substitute the number 1 for x and the number 2 for y in the equation, we get {{{2=2(1)}}} or just {{{2=2}}} which we know to be a true statement.  But let's look at the point (5,1).  If we substitute the x-coordinate, 5, and the y-coordinate, 1 into the equation we get {{{1=2(5)}}} or {{{1 = 10}}}, clearly a false statement.  So we can say with certainty that the point (5,1) does not lie on the line.


For your problem, you are faced with having to determine, for part a, what value of x will make the equation {{{2x+1/5y=6}}} true whenever y has the value 20.  So let's put 20 into the equation and see what happens:


{{{2x+(1/5)(20)=6}}}


{{{2x + 4 = 6}}}


{{{2x = 2}}}


{{{x=1}}}


You should be able to tackle part b by yourself now.  Write back if you are still stuck.