Using an algebraic method, but continuing with the same equations:

Set 3x equal to 2x+6. Your goal is to solve for x, so subtract 2x from both sides to get x on one side of the equation. Once you have subtracted 2x from both sides of the equation, you’re left with x=6. Notice, this is the same value Desmos calculated in part a. Once you know the x-value, you can substitute it into either equation to solve for the y-value. For example, since y=3x we can substitute x in to give us y=3(6) which results in the y-value of 18.

Similarly, for the other equation, since x=6, y=2(6) +6 which results in the same value of 18. Therefore, your solution, also known as the point of intersection, is x=6 and y=18.

You can find the solutions to other linear equations using either Desmos or the algebraic method, but one way may prove to be easier or more challenging than the other. It is important to keep in mind that not all systems of equations have solutions. This occurs when the lines do not have a point of intersection, i.e. they have the same slope.

Now that we have analyzed part a and b, we will finish up with part c; solve real-world and mathematical problems leading to two linear equations in two variables.