help me solve these systems!?

Question

with substitution

2x+3y=7
4x-5y=25

with elimnation

x+y=13
x-y=5


&

2x=3y=7
4x-5y=25

and can i have steps to. i want to learn.

sry for posting all this math. i dont get this linear equation stuff

Answer 1

For substitution you have to solve the first equation for either variable and then plug it into the second equation. We will solve for x.

2x + 3y = 7
2x = 7 - 3y
x = (7-3y)/2

Now we plug it into the second equation for x.

4((7-3y)/2) - 5y = 25
2(7-3y) - 5y = 25
14 - 6y - 5y = 25
-11y = 11
y = -1

Now that we have y, we can plug it into either equation and solve for x to find x.

2x + 3(-1) = 7
2x = 10
x = 5

The answer is x = 5 and y = -1.

For elimination you need to eliminate a variable by adding the two equations together.

x + y = 13
x - y = 25

Add them vertically and you get:

2x = 38
x = 19

Plug x into the equation to find y.

19 + y = 13
y = -6

The answer is x = 19 and y = -6.

For the last equation I'm assuming you meant 2x + 3y = 7. We want to multiply one of the equations by a constant so that when we add the 2, one of the variables will be eliminated.

We have:

2x +3y = 7
4x -5x = 25

We are going to multiply the first equation by -2 so that 2x will become -4x and it will be eliminated when we add it to the 4x from the second equation.

-2(2x + 3y) = -2(7)

-4x -6y = -14
4x - 5y = 25

We add them vertically to get:

-11y = 11

y = -1

We plug y into one equation to get x.

4x -5(-1) = 25
4x = 20
x = 5

The answer is: x = 5 and y = -1.

I hope this was helpful!

Answer 2

Sorry, try again...

Substitution

x = (7-3y)/2
4((7-3y)/2-5y = 25
2(7-3y)-5y = 25
14 - 6y - 5y = 25
14-11y = 25
-11y = 11
y = -1

2x + 3(-1) = 7
2x = 10
x = 5

Elimination... Good resource: http://www.teacherschoice.com.au/Maths_Library/Algebra/Alg_10.htm

2x+3y=7
4x-5y=25

If you look at the example on the website I provided, you'll see that sometimes you can't add both equations and cancel them, you need
to multiply them so one of the variables will be cancelled-out.

So...
(5)(2x+3y)=(5)7
(3)(4x-5y)=(3)25

10x + 15y = 35
12x - 15y = 75

We are able to use elimination now since we can cancel out the y component...

10x + 15y + 12x - 15y = 35 + 75
22x = 110
x = 5

Plugin x to the original equation
2x+3y=7
2(5) + 3y = 7
10 + 3y = 7
3y = -3
y = -1

Answer 3

substituion means solve for one variable and plug it back in.

2x+3y=7
4x-5y=25

solve for x (or y) to get x = (7 - 3y)/2

and plug into the second equation like so

4 ( (7 - 3y)/2 ) - 5y = 25

you can do that algebra right?


I dont like the elimination method so I wont talk about that one.

just solve for one variable, put it in the other of the two linear equations and then just solve for the one variable that is left.

works for me

Answer 4

ok for the first problem involving substitution you need to get an x by itself

ill start off with 2x+3y=7

subtract 3y to get 2x by itself

2x=7-3y
now divide by 2 to get x alone

x= (7-3y) / 2

ok now we have one value of x byitself
now for the substitution
4x-5y=25
put x=(7-3y) into the second equation

4((7-3y)/2)-5y=25

now distribute the 4

(28-12y/2)-5y=25
14-6y-5y=25

group like terms

-11y+14=25

get -11y by itself by subtracting 14

-11y=11

divide by -11

y=11/-11


and you have y=-1

substitute that into the x equation and solve

x=7-3y/2

x=7-3(-1)/2

x=10/2
x=5
ther you go
-----------------------------------------------------------

for the elimination i will explain the first one in detail and you can solve the second

elimination is much like addition of equtions

look at it this way:

x+y=13
+ x-y=5
------------
2x=18

see how the +y and the -y cancel out

then you get x=9

you can put that in an equation and get y

for the second problem the key is arranging all the terms such that everything lines up it will make it alot easier
dont get frustrated if you have trouble mssg me good luck!

Answer 5

Using substitution means you have to solve one of the equations for a single variable.
2x+3y=7
2x = 7 - 3y
x = 7/2 - 3/2 y

Then substitute x in your second equation with what we now know x equals in the above equation.

for elimination you can add the 2 equations together
x + y = 13
x - y = 5
-------------
2x + 0 = 18

then solve for x

Answer 6

1.2x=7-3y
x=(7-3y)/2
substituting in the second equation
4(7-3y)/2-5y=25
4(7-3y)-10y=50
28-22y=50
22y=-22
y=-1
sub in 1st equation
x=(7+3)/2
x=5

2.adding
2x=18
x=9
substituting in(1)
y=4

3.2x+3y=7 int0 2
4x+6y=14
4x-5y=25
subtracting
11y=-11
y=-1
2x-3=7
2x=10
x=5