MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
If two equations are both in slope-intercept form, you can easily using substitution to solve the system by putting one value of y equal to the other value of y (since in both equations, y is equal to something). From there, use inverse operations to solve for x. Once you have the value for x, plug it into either of the two original equations in the system to find the value of y. The x and y values make up the coordinate point of the solution to the system. Check your answer by plugging the x and y value into both equations to see if they are both true.
This problem using substitution is going to be not too difficult because I have 2 equations that are both already solved for y. Since I know y is equal to the expression 3x plus 1, and y is also equal to the expression 2x minus 3, it makes sense mathematically to write 3x plus 1 equals 2x minus 3. That guy is equal to y and that guy is also equal to y, so I’m just substituting those two equations so they look like one equation with one variable.
Now this is a straight forward solving problem. I’m going to find x, and then go back and find my y value. Here we go if I want to find x, I’m going to subtract 2 Xs from both sides, so now I have x plus 1 equals -3. Now I need to get x all by itself by subtracting 1 from both sides, x is equal to -4. Keep in mind that’s only going to be half of my answer. I’m going to put a box around this like I would have with my whole answer keeping in mind I still need to find what that y value is.
In order to find y, I’m going to take x equals -4, and substitute it into either original equation, that way I’ll get my y value, and I’ll go back and check in a second. I’m just going to choose to use the first equation. I could also use the second one and I’ll still get the same answer for y. Y is equal to 3 times my x quantity plus 1, so y is equal to -11 oops, that’s a +1 right there, plus 1 okay. Y is equal to -11. I’m pretty sure that’s my answer, I’m pretty sure that’s the point where these lines cross even though I didn’t graph them .
In order to check my work, I’m going to go back and plug in -4 for x and -11 to y into both original equations and make sure I get equalities. So here comes my check, first I’m going to check it in the first equation, is it true that my y quantity is equal to 3 times my x quantity plus 1? Let’s see -11 equals -12 plus 1, yap that’s true. Good so I’m half way there, I think it's right. I also need to check it into the second equation.
My y quantity I hope is equal to 2 times my x quantity take away 3. -8 take away 3 yap good. That’s how I know I did this problem correctly. Even if your textbook didn’t ask you to check your work it’s always a good idea to do this process, it only takes about a minute maybe less and that way you’re going to make sure you get A pluses on your homework and also on your tests.
