How do I solve a system of equations by substitution if both equations are in y=mx+b form?

Question

I really can't figure it out :(

Answer 1

Since both equations are written as "y=...", you can set the equations equal to each other and solve for X. This works because if both equations equal the same unknown y value, then they must also equal each other. For example, suppose you are asked to solve the system of equations: y = 2x + 3 and y = 4x + 1.  Begin by realizing that since y represents the same number in both equations, then both equations must equal each other, so you can write: 2x + 1 = 4x + 3. If this is still confusing, imagine that y is actually a number, let's say 5. If 2x+3=5 and 4x+1=5, then (2x+3) must equal (4x+1), because both equal 5. What you are doing here is substituting the value of y found in the first equation into the second equation. Once you have the two equations set equal to each other, you can solve for X. Going back to my original example of 2x+3=4x+1, you would first work to get all of the X terms on one side of the equation, so subtract 2X from both sides. You will be left with 3=2x+1. Now subtract one from both sides, to get your X term by itself, resulting in 2=2x. Finally, divide both sides of the equation by two and you will get the answer, X=1. To solve for Y, you can plug in the value of X that you just found (X=1) into either of your original equations. So both y=2(1)+3 and y=4(1)+1 will give you the same answer: y=5. This assumes that you know or are able to figure out your slope for both equations. Please let me know if you have any further questions. I hope this helped.