whats the answer to this?

Question

2y+3x=13
-x+y= -1

Answer 1

*There are 4 ways to solve this - the substitution method is fast and easy :-) *Take either equation and solve for "x" or "y" > let's solve for "y" in the 2nd equation.

First: add "x" to both sides (opposite side means opposite sign) >>>

- x + x + y = x - 1
y = x - 1

Sec: take (x - 1) and replace it with "y" in the 1st equation >

2(x - 1) + 3x = 13
2x - 2 + 3x = 13
5x - 2 = 13
5x - 2 + 2 = 13 + 2
5x = 15
5x/5 = 15/5
x = 3

Third: replace 3 with the "x" variable in the sec equation >

- 3 + y = -1
- 3 + 3 + y = -1 + 3
y = 2

(3, 2)

Answer 2

There are many ways to do this sort of problem. Here are two of the main ones:

1. Substitution. From the second equation, write y = -1 + x. Substitute this expression for y in the first equation. Then you get
2(-1 + x) + 3x = 13
=> -2 + 2x + 3x = 13
=> 5x = 13 + 2
=> x = 3
and since y = -1 + x, y = 2.

2. Reduction. The idea here is to cancel out either the x or the y terms, by adding (or subtracting) a suitable multiple of one equation to the other (this is perfectly OK from a mathematical viewpoint).
To cancel out the y terms, for instance, since we have 2y in the first equation and y in the second, we subtract twice the second equation from the first:
2y + 3x - 2(-x + y) = 13 - 2(-1)
Normally this line would be skipped and we would move straight to:
5x = 15
=> x = 3
Then this value is substituted into either of the original equations to determine y. You can also do this in the reverse order to eliminate x first, find y, and then substitute for x.

This method may seem more complicated, but with practice it is generally easier and faster than the first.

Answer 3

2y + 3x = 13- - - - - -Equation 1
- x + y = - 1-- - - - -- Equation 2
- - - - - - - - -

Substitute Method Equation 2

- x + y = - 1

- x + y + x = - 1 + x

y = - 1 + x

The answer is y = - 1 + x

Insert the y value into equation 1
- - - - - - - - - - - - - - - - - - - - - -

2y + 3x = 13

2(- 1 + x) + 3x = 13

- 2 + 2x + 3x = 13

- 2 + 5x = 13

- 2 + 5x + 2 = 13 + 2

5x = 15

5x / 5 = 15 / 5

x = 3

The answer is x = 3

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - -

2y + 3x = 13

2y + 3(3) = 13

2y + 9 = 13

2y + 9 - 9 = 13 - 9

2y = 4

2y / 2 = 4 / 2

y = 2

The answer is y = 2

Insert the y value into equation 1

- - - - - - - - - - - - - - - - - - - - -

Check for equation 1

2y + 3x = 13

2(2) + 3(3) = 13

4 + 9 = 13

13 = 13

- - - - - - - - -

Check for equation 2

- x + y = - 1

- 3 + 2 = - 1

- 1 = - 1

- - - - - - - - - - -

The solution set is { 3, 2 }

- - - - - - - - - -s-

Answer 4

x = 3, y = 2

Answer 5

Math homework obviously.... since you can't work with two variables, find one in terms of the other:

- x + y = -1
- x = - 1 - y
x = 1 + y

Then you substitute it and get:

2y + 3(1 + y) = 13

Simplify it to get:

2y + 3 + 3y = 13
5y + 3 = 13
5y = 10
y = 2

You have y = 2, then you want to get x which is equal to y + 1:

x = y + 1
x = 2 + 1
x = 3

y = 2 and x = 3

Answer 6

(2y+3x=13
(-x+y= -1

y = -1+x
2(-1+x) + 3x = 13
-2 + 2x + 3x - 13 = 0
5x = 15
x = 15:5
x = 3

y = -1+x
y = -1+3
y = 2
Solution: {x, y elements of R | x = 3 and y = 2}
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Answer 7

Y=5 and x=-6

Answer 8

2y+3x+13 -------Equation 1
-x+y=-1 ----------Equation 2

From Equation 2,
-x+y=-1
y=-1+x
y+1=x ---------Equation 3


Substitute this into Equation 1 and solve
2y+3x=13
2y+3(y+1)=13
2y+3y+3=13
5y=13-3
5y=10
y=10/5
y=2

and

Subsitute y=2 into Equation 3 to find x
x=y+1
x=2+1
x=3


Substitue into the origin equation
2y+3x=13
2(2)+3(3)=13
4+9=13
13=13

and

-x+y=-1
-3+2=-1
-1=-1

Answer : x=3 and y =2

Answer 9

2y+3x=13
-x+y= -1

-x+y=-1
y= -1+x

2y+3x=13
2(-1+x)+3x=13
-2+2x+3x=13
5x=15
x=3

-x+y=-1
-3+y=-1
y=-1+3
y=2

Answer 10

2y+3x=13
-3x -3x
2y=13-3x
2y/2=13-3x/2
y=(13-3x)/2

this is a graphing prob so you have to find a number for x and work out the equation to get y and then graph it!