How do you solve each system?!??

Question

I have a huge midterm tomorrow and im trying my best to study now but i dont know how to do it?!?

the directions say "solve each system by subsitiuion"
example:

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

plz explain how to solve by subsitiutiong for x and y?

Answer 1

9x - 6y = 21
2x + 6y = - 10------ADD

11x = 11
x = 1

1 + 3y = - 5
3y = - 6
y = - 2

x = 1 , y = - 2

Answer 2

To solve by substituting, find the equation with a variable "all alone" in this case it would be the 2nd equation

x+3y= -5 --> now solve the equation for that variable

subtract 3y from BOTH sides

x= -5 - 3y ( you can't but -5 & -3y together b/c they are NOT like terms)

Now go back to the 1st equation 3x - 2y =7

Where you see x plug in what x equals from the 1st equation

3 ( -5 -3y) - 2y = 7

Now distribute

-15 - 9y -2y =7

Combine like terms

-15 -11y= 7

-11y= 7+15
-11y = 22

y= -2

Now we need to find the X value
go back to either equation
x+ 3y = -5 is the easiest

we know what y is it's -2

x + 3 (-2) = -5

x -6 = -5

x = 1
The solution or POINT OF INTERSECTION of the system is the point ( 1, -2)

Answer 3

first solve for x or y in one of the problems. ex: x=-5-3y . You then plug that in for x in the other problem:
3(-5-3y)-2y=7. > -15 - 9y - 2y=7 > -15 - 11y=7 > -11y=22 > y=-2. you then plug y into the other equation to get x.
x + 3(-2) = -5 > x - 6=-5 > x=1

Answer 4

first, Isolate a variable. In this example the second equation looks easy to isolate x+3y=5 can be quickly switched to


x+3y-3y=5-3y
x=5-3y.

Now sub in that equation for the x in the top portion to solve for Y. Then simply move your Y value to the bottom equation and solve for X!

Good luck!

Answer 5

x = -3y -5

3(-3y -5) - 2y = 7
-9y - 15 - 2y = 7
-11y = 22
y = -2

x = -3(-2) -5
x = 6 -5
x = 1

Check:

3(1) - 2(-2) = 7 and 1 + 3(-2) = -5
3 + 4 = 7 and 1 - 6 = -5
7 = 7 and -5 = -5

And they work out

Answer 6

Substution means to change x or y from one equation to other one.
For example, we will subtitute x of first equation on the second equation:

In the first equation, calculate x
It's x = (7+2y)/3
Then, write this result on the x in the second equation.
It's (7+2y)/3 + 3y = -5
Now, calculate the y.
It must result you y = -2
Finally, in the equation x = (7+2y)/3 , replace y by -2 and calculate x. It's x = 1
ok?

You can do it first with x or first with y, and begin with any of two equations.

I hope that you understand me my english... I'm chilean...xD!
Good luck!

Answer 7

Oooh, these are easy. y=3x+2 y=3x-4 3x+2=3x-4 (set equal to each other to eliminate "y" and solve for "x") -2 -2 (subtract 2 from both sides) ------------------ 3x =3x-6(now subtract 3x from both sides) -3x -3x ---------------- 0=-6 (these are unequal so this is an impossible solution I also agree with "kindrick..." that the lines would be parallel meaning that they will never cross, therefore the reason that there will be no solution/no real numbers.

Answer 8

solve and substitute
3x-2y=7
x+3y=-5
In the second equation, x = -5-3y
So put this into the first equation instead of x
3(-5-3y) -2y = 7
Now solve for y
-15-5y = 7
y = - 4.8
No substitue this into second equation
x + 3(-4.8) = -5
x = 7.4

Answer 9

you would use a number to substitute for x then solve for y... and vis versa...

example

3x-2y=7
substitute x for 1
3(1)-2y=7
3-2y=7
then subtract 3 from each side
2y=4
then divide 2 by both sides
y=2

GOOD LUCK! hope this helps but its hard to explain with typing

Answer 10

3(-3y-5)=7
-9y+15=7
find y, sub in for it in one of the original systems.