this week in math we learned about solving a system using elimination. To solve a system using elimination you first take the 2 equations: 3x + 4y = 10, -x + 5 = -16. now you should multiply the second equation by 3 to make it -3x and the first equation is 3x so they cancel each other out to get: 4y = 10, +15y = -48(because you multiplied everything by 3 on the second equation). now add the like terms from the equations to get: 19y = -38. now you divide both sides by 19 to get y = -2. now put the -2 into the equation to have 3x + 4(-2) = 10 multiply to get: 3x – 8 = 10. bring the -8 to the other side of the equation to get: 3x = 18. divide both sides by 3 to get x = 6. and that’s how you solve the equation.

this week in math we learned about systems in linear equations. A system in a linear equation is where 2 lines meet. You can solve this by taking the 2 equations, x + 2 = y and 3x + 4y = 1. you need to get a variable by its self on one side of the equation like y in x + 2 = y. Now, you have to put the x + 2 into the other equation in place of the y so you would get 3x + 4(x + 2) = 1 and then expand it to get 3x + 4x + 8 = 1 and add the like terms  but put the numbers without a variable to the other side of the equation to get 7x = -7 and now divide to get x = -1. To get the y you need to add the x into one of the equations (the first one is easier) to get -1 + 2 = y and solve to get y = 1.

this week in math we learned how to make 2 points ((7,5) and (6,1)) on a graph into a general equation. First, you need to find the slope of the 2 points, to do this you need to subtract the 2 x’s and 2 y’s from each other but make sure you subtract the second point by the first point. ( so 1-5 and 6-7 to get -4/-1, y goes on top) now you put the slope in front of the x and subtract the x by one of the x points ( -4/-1(x – 7)) and on the other side of the equals sign subtract y by the same point on the y-axis. ( -4/-1(x-7) = y – 5) and now the equation is in point-slope form. to turn it into general form you need to distribute the slope. ( -4x + 28 = y – 5) Move everything on one side of the equation to the other and switch the sing of it, now add the like terms and the equation is in general form.(-4x – y + 23 = 0)

this week in math we learned about the slope of a graph. in order to find the slope of a graph, you need to take the graph.
now, find 2 points on the graph where it goes on both an x and a y line like these ones: 

now you need to find how much you need to rise up from the first point to be on the same level as the second point and how much you need to go right to get to the second point like this: 

now you have to put the rise over the run so you would get 6/5 and that is your slope.

this week in math we learned how to find the distance and middle between 2 points of a graph. To find the middle between 2 points you first have to take the 2 coordinates (4,6) (8,5) add the x and last numbers of each pair together 4 + 8, 6 + 5, and divide the answer by 2. 12/2, 11/2 = (6, 5.5). to get the length between 2 points you can use a² + b² = c². take 2 points on a graph (-3,8) (6,-4) and find the distance between the x and y by subtracting them -3 – 6 = 9, 8 – -4 = 12 (9,12). now put them in the equation and square them 9² + 12² = c². 81 + 144 = 225. now find the square root of your answer. √255 = 15

this week in math we learned about how to determine if something is a function or just a relation. if its a function then an input will not have a different output every time you input the independent variable. Like this: See how the two 4 inputs have different outputs(7 and 14)

how you see  this on a graph is to see if anything on the x axis over laps each other. like this:  See on the 2 graphs that aren’t a function you can draw a vertical line and it would go through 2 lines. but if you drew a line on the one that is a function it would only go through 1 line.

this week in math we learned about domain and range in a graph. the domain of a graph is where the line or the points are confined to in the x axis, range is the same but with the y axis. you can find the domain by taking this graph

and seeing where the most left of the red line is. Take that point, draw a line up and down the graph like a wall that the line can’t pass and see what the x is for the wall(-3). you can use an equation like this: -3 ≤ x. that isn’t completed yet, the other side of x is missing. what you do to get the other side of x is take the most right point of the line and make a wall there too. take the number for x and you get -3 ≤ x ≤ 2. the graph should look like this

to get the range you do the same as the domain but with the y axis. take the most bottom point of the line and instead of seeing where the x is and drawing a vertical line, you need to see where the y is and draw a horizontal line like a roof and a floor. you would get -2 ≤ y. do the same to the top and you get -2 ≤ y ≤ 2.

this week in math we learned about x and y intercepts. an x intercept is when a point on a graph has a value of 0 for x, the intercept for y is when a point on a graph has a value of 0 for y.

but you can use a trick to find out what the other value is going to be on the graph. take y = 12 – 3x for example. in order to find out the value of x on the y intercept you make the y a 0 so you have 0 = 12 – 3x. now you have to balance the 2 sides by subtracting 12 to cancel the 12 on the side with the x but what you do to one side you have do to the other so the equation will look like -12 = -3x. now you can divide the x by -3 to get the x by it’s self but that means you also have to divide the -12 by -3. after you do that the equation is 4 = x the x will equal 4 when y equals 0.