How to find the intersection point of two linear equations

okay um if i was gonna be solving a problem like this what it wants us to do is it wants us to find the intersection of the two points so what we're gonna need to do is see when will these two equations you know equal each other when will they cross so what we'll look at is you know if we said something like this okay where are their points going to be exactly the same so if you think of this here's your y and here's your x right so what i'm saying is at this intersection point the x value and the y value are going to equal each other for both the um for both equations so what i'm saying is what we're going to do is we have two different equations we want to find when does the x value equal the y value so mrs garvin would you please come to the main office mrs garvin please come to the main office and not go to r9 portal r9 also officer smith would you please come to the conference room would you please come to the principal's conference room officer smith okay um so then to go and figure this out what we're going to have to do video yeah just come by and say hi i want to see what you're doing right now okay we're doing intersections with two lines will you just sit down i'll be on with done with this video in two seconds thank you for showing me what you're doing um so then what we're gonna want to do is here let's solve for y so if i subtract the x on both sides i get y equals a negative x plus three okay so now if i want to set these equal to each other right i want to say well i know that my y values have to be the same for both of these equations my two y values have to be exactly the same so therefore what i'm going to do is i'm going to plug this equation into the other one so i'll obtain 3x minus 2 times negative x plus 3 equals 4. all right then what i can do is when the y values are the same meaning i plugged one y value to the other one i can find when will the x values be the same so i'll use distributive property to give me 3x plus a 2x negative 2 times negative x gives you positive 2x minus 6 equals 4. combine my like terms to give me 5x minus 6 equals 4 add 6 5x equals 10 divided by 5 x equals 2. so what that tells me is when my y values are equal to each other my x value is equal to 2. so now the next thing i need to do is now well if x equals 2 what is my y value for both those problems so let's go and take a look at that what i can do is i can plug 2 in for x and figure out what my y is going to be so i'm going to plug it into both equations so you guys can see that when x equals 2 my y values are going to be exactly the same and that also will figure out what the y value is so i plug in 2 plus y equals 3. subtract 2 y equals 1. and we'll say that value is 1. or you could have plugged it in this equation 3 times two minus two y equals four three times two is six minus two y equals four subtract six negative two y equals a negative two divided by negative 2 y equals 1. so again remember when you're dealing with intersection you want to set your equations equal to each other plug one equation in for the other so y equals x minus 3. so therefore i'm going to plug that in solve for my one variable x then once i know the value of x where the two equations meet i can plug that into either one of the equations and i'll find the y value for when the two equations mean and that's how you find the intersection of two points