ALGEBRA help?

Question

i dont know how to do this:
-x - y = 15
4x - y = -5

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

i need to know
x & y

example:
(x,y)

Answer 1

In short, the answers are:
#1 : x = -4, y = -11
#2 : x = 4, y = -1

How do you get them? They are done in groups, because the x's and y's in each group are equal. You solve them by adding or subtracting, as appropriate, and multiplying by some number to make sure you can add/subtract to eliminate either the x or the y.

example:

- x - y = 15
4x - y = -5

if you subtract the bottom from the top,

- x - y = 15 which is equivalent to -x - y = 15
- (4x - y = -5) -4x + y = 5

therefore, by adding them,
-y +y = 0

or -5x = 20; x = -4. Then you plug in for x in either equation and solve for y.

A hint for the second problem, mulitply one of the equations by -5.

Good luck.

Answer 2

If you have a graphing calulator, you can do it a really simple way my teacher taught me. Open a matrix, set the frame to 2 by 3. The plug in the coefficients of each number (-1 -1 15) in the first line and (4 -1 -5) in the second line. Then 2nd quit. Then go back and find the button that says rref( and click it. then plug in the letter of the matrix that you saved it under, probably a. It will give you a screen that looks like this with the answer:
[[1 0 -4]
[0 1 -11]]
The x answer is -4 and the y answer is -11

Just sharing a shortcut I learned

Answer 3

Okay, you combine the two equations and solve. In the first one, you change the signs so you can combine them and get rid of the y:
x+y=-15
4x-y=-5
Now that you've changed the signs, add them, and you get 5x=-20, or x=-4.
Now that you have the value of x, plug it into either of the original formulas, and you find that y=-11.

In the second example, first let's get the letters all on one side, and we have:
2x+y=7
3x+5y=7
We need to get rid of either the x's or the y's. In this case we can get rid of the y's, but first we have to multiply the top equation by -5. We do that and get:
-10x-5y=-35
3x+5y=7
Now we combine them and get -7x=-28, or, x=4. Plug that into either formula to find that y=-1.

Answer 4

Well there are several methods, though I prefer substitution.

In the first one, solve for either x or y in one of the equations so
-x-y=15
-y=15+x
y=-15-x
Now plug it in into the second equation
4x-(-15-x)=-5
4x+15+x=-5
5x=-20
x=-4
Plug back the x value into either equation
-(-4)-y=15
-y=11
y=-11

One could also plug both equations into a graphing calculator to see where they intersect, but do that only to check.

In the second one, the first equation is already solved for y, so just plug 7-2x into the second and simplify.

Answer 5

1. x=2
2. x=4

Answer 6

(1) -x-y = 15
x=-15-y

(2)4x-y=-5
y=4x+5

substitute y to equation (1)
x=-15-(4x+5)
x=-15-4x-5
x=-4x-20
x+4x=-20
5x=-20
(5x=-20)/5
x=-4

now, substitute the value of x to equation 2
y=4x+5
y=4(-4)+5
y=-16+5
y=-11

____________________________

(1)y = 7 - 2x

(2)5y= -3x +7

substitute the value of y to equation (2)
5(7-2x) = -3x+7
35-10x = -3x+7
-10x+3x=7-35
-7x=-28
(-7x=-28)-7
x=4

substitute the value of x to equation (1)
y= 7 - 2x
y=7-2(4)
y=7-8
y=-1


____________________
Therefore
on the first problem
x = -4
y = -11

ont the second problem
x = 4
y = -1

Answer 7

-x -y =15
4x-y =-5
subtract one equation from the other so
4x - (-x) =5x -Y- (-y)= -y+y = 0 15-(-5)=20
so you have 5x+0=20
5x=20 20/5=x x=4
then - 4(4)-y=-5 16-y=-5 -y=-21 y=21

so x = 4 and y = 21

Answer 8

add x to both sides of the first equation

-y=x+15

Sub in for -y in the next equation

4x+x+15=-5

-15 from both sides

5x=-20

x=-4

sub back into first equation

4-y=15
sub 4 from both sides
-y=11
multiply by -1
y=-11

sub in for y

5(7-2x)=-3x+7
distribute
35-10x=-3x+7
subtract 7 from both sides
28-10x=-3x
add 10x to both sides
28=7x
divide by seven
x=4

sub back into first equation
7-2(4)=y
7-8=y
y=-1

voila!!!

Answer 9

ok...lets c....
-x - y=15
-y=x+15
y=-x-15
fill in y in the second part, then u will figure out x, and ull hav ur answer.
4x-(-x)-15=-5
5x=10
x=5



y=7-2x
5(7-2x)=-3x +7
35-10x=-3x +7
28=7x
x=4.....fill in 4 for x, and u get y...good luck

Answer 10

are they two separate ones?

This is a system of equations.

Solve the first one for y.

y=15+x

then plug into 4x-y=-5

So ---> 4x-(15+x)=0

solve for x (distribute, order of opperations)

same process for second one.

substitute y=7-2x into 5y=-3x+7 and solve for x.