another crazy solve system w/ substitution?

Question

1. x+y = 4
2x +3y =9

Answer is obvious but I need to know how to figure it out...

Answer 1

First, you need to decide which one you are going to solve for first.I solved for y, but you can decide to solve for x instead, it's exactly the same thing.

So first, you solve one of the equations for one of the variables:

x = 4-y

Then you substitute that back into the other equation, so that you're only going to have one variable:

2(4-y) + 3y = 9
8 - 2y + 3y = 9
y =1

Then plug that back into the other equation to get that x = 3. To check your work, re-plug that back into the second equation and see that it does equal nine.

So your answer is

(3,1)

Answer 2

x+y = 4
2x + 3y = 9

isolate x:
x+y = 4

subtract y from both sides of the equation:
x+y-y = 4-y
you get:
x = 4-y

substitute x = 4-y into 2x + 3y = 9

2x + 3y = 9
2 * (4-y) + 3y = 9

distribute 2 by multiplying 4-y:

2*4 - 2y + 3y = 9
8 -2y + 3y = 9
8 + y = 9

subtract 8 from both sides of the equation to isolate y:

8+y-8 = 9-8
y = 1

plug y's value (1) into x = 4-y to get x

x = 4-y; y=1
x = 4-1
x = 3

so: x=3 and y=1

Answer 3

you can either substitute or linear combinations

substitution
1. x= 4-y

2( 4-y) +3y =9
8-2y+3y=9
8+y=9
y=1

x=4-1
x=3

or

linear combination
-2(x+y=4)
2x +3y= 9

-2x -2y= -8
2x +3y = 9

y=1

2x +3= 9
2x =6
x=3

so in both methods you isolate one variable by taking the other variable out. In substitution you solve for either x or y and plug whatever you got into the other equation and you solve for whatever. In linear combination add both equations together but first multiply an equation or both equations to try to cancel out a variable and then solve regularly

Answer 4

I have it.. editing post wait..

1. Multiply x+y=4 by -2
2. The x's cancel out, so combine the two equations with just the y's and the numbers. (4y=13)
3. Divide 13 by 4, and you have your y value.
4. substitute the y in for all of the y's and solve for x!

Answer 5

1. x+y = 4
2x +3y =9
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very easy.

1. you just have :
x=1 and y=3
x=2 and y=2


2. you just have :
x=3 and y=2

you have that because if you do 3x2=6 and add that it 3 you get 9.