Help with substitution (Algebra 2)?

For substitution:

You need to get at least one of the equations into a suitable form so you can plug it into the other one, and find the value of one of the variables, then you must plug what that variable equals into the equation to find what the other one is. Let me show you.

x+2y=4

3x-y=5 (I chose to rearrange this one.) So -> You subtract 3x from one side. (-y=5-3x) But you're not done, you've still got a -y on the other side, and it needs to be positive. So you divide by negative one which gives you (y=3x-5) (I rearranged them in different orders so it doesn't look stupid, but you can do whatever with them.)

So now that you've got y=3x-5 you have to plug this into the other equation where "Y" Is.

So: x+2(3x-5)=4

Solve this by distribution, using order of operations.

This gives you x+6x-10=4, Now you combine like terms. This would give you 7x-10=4

Time to Solve it, You add 10 to both sides, and then divide by 7, which gives you x=2.

Take one of the original equations, and plug 2 in where there's an X.

(2)+2y=4 -> Solve it! -> 2y=2 (subtract 2 from the other side) and Y=1.

Answer, y=1 x=2.

FOR SOLVE BY GRAPHING:

All you have to do is get each equation into slope intercept form, and then plug it into your graphing calculator and see what it does, and then find the point of intersection.

Hi.

For the first problem:

x+2y=4

3x-y=5

Plug in 2 for x and 1 for y and that is a match

Solve by graphing:

Put the equations in slope intercept form: 2x + y = 9 becomes:

y =9 - 2x

Same for the second eq. and then just graph normally. Their point of intersection is their solution (2,5) ; x = 2 and y = 5.

Solve by the substitution method:

2x+y= 5

4x+3y= 7

Solve the first one for y:

y = 5 - 2x

Then plug that in for y in the second one:

4x + 3(5-2x) = 7

4x + 15 - 6x = 7

-2x = - 8

x = 4

Then plug that value into either eq to find out what y equals: y = -3

1.

yes, plug in the numbers and BOTH equations should be true.

let's see:

2 + 2*1 = 4

3*2-1 = 5

so, yes, (2,1) is a solution

2. for graph, u need to plot those two equation on X Y plot and see where they intersect.

now, the trick is to plot these, right? well, they are liniar equations so the plots will be lines. for one line you need two points.

let's look at the 1st one:

2x+y=9

and find two points.

say x = 0, then y = 9

another one y = 0 then x = 9/2

so the two points would be (0,9) and (9/2,0).

3. this is quick

2x+y= 5

4x+3y= 7

get from 1st eq y = 5-2x

and plug it in the second

;-)