



 
We have two solutions for you Hi Lily, Let's consider a hypothetical example. Suppose that you have two linear equations in the variables x and y and you solve the first equation for x and obtain
You then substitute this expression for x into the second equation to obtain an equation in the variable y. You then proceed to solve this equation for y and you end with 0 = 0. What this means is that if you have the pair (x, y) that satisfy x = 5 + 3y then (x, y) satisfies the second equation also because it yields the true statement 0 = 0. Thus you can choose any value for y, find x using x = 5 + 3y and the pair (x, y) is a solution to both equations. Thus you have a system with infinitely many solutions. You might however have solved the first equation for x yielding
and ten substituted into the second equation to obtain 0 = 5. What this means is that no pair (x, y) that satisfies x = 5 + 3y can also satisfy the second equation so the system has no solutions. I hope this helps,
Hi Lily. Here's a simple example of two parallel lines (I know they are y = 5x 5x = 5x + 1 What if the two lines are identical? 5x = 5x Hope this helps,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 