So if Y is equal to two X, wherever I see Y in the other equation, I can replace it, I can Well, in the other equation I could substitute for that variable that has been solved for. All right, now there's several ways that you could approach it, but the way I like to thinkĪbout it right when I look at it is if in one of the equations I've already explicitly What is the value of X? Pause this video and have a go at it before we work through it together. The system of equations above has solution X, Y. Graphing is probably the easiest, safest and fastest way to answer this question, but solving gave us the same answer. If the lines are parallel (never crossing) they have NO solutions. Since they are two lines, they CANNOT have two solutions-two lines can cross one time or can coincide (be duplicates of the same line) in which they have the same solutions at an infinity of places. He quickly graphed the lines to show that they intersect at (0, 0) which is the same solution we found be solving. Sal decided to use the fact that this is a system of linear equations, which means it represents two lines. So there is one solution and it also explains why y can equal 9y. Plug that into your original equation to find out that when y = 0, x = 0 Instead you need to use algebra to isolate the y by subtracting y from both sides: You might be tempted to say IMPOSSIBLE! y cannot equal 9y If you substitute the value for x into the equation for y you get y = 3 (3y) If you try substitution to solve this system, you get some strange equations. If you are able to get any solution, you CAN say that the "zero solutions option" is not correctĪnother reason it would be tricky to solve is that this problem is tricky to solve. The answer is whether there are two solutions, only one solution, no solutions or infinite solutions. The answer is not the number that you would get when you solved the equations.
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