There are technically 2 different ways that you could go about solving this problem. The first option is definitely the easier way to solve this problem because it is completely visual - unless you prefer to solve things algebraically. The first way to solve this problem would be just to graph the two equations in a graphing calculator. (If you do not have one, I would reccomend using the wesite Desmos. It is a free online graphing calculator.)
When you graph the two equations, look to see how many times they intersect or meet at the same point. If this only occurs once, then there is only one solution. If they meet at two points, then there are two solutions. If the 2 equations overlap each other when they are graphed, then there are infinitely many solutions. If the 2 equations do not touch at all on the graph, then there is no solution. In this case, when you graph the 2 eqations you only see one place where both equations meet at the same point. That point is (8,3).
Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution.
5/4x − 2/3y = 8
1/4x + 5/3y = 7
Find the solution, if one exists.
1 answer
1 answer