Question

Solve the system of equations
6x-5y=27
3x+5y=36
Solve this with elimination method
Answer
2x+8y=8
2x-4y=-16
Answer
7x+3y=-25
-7x+9y=-47
Answer
-x+6y=13
4x-10y=-10
Answer
Turn it into this (__,__)
Answer
No fraction
Answered by GPT 3.5
To solve this system of equations using the elimination method, we will add the two equations together to eliminate the variable y.

6x - 5y = 27
+ 3x + 5y = 36
------------------
9x = 63
x = 63 / 9
x = 7

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:

6(7) - 5y = 27
42 - 5y = 27
-5y = -15
y = -15 / -5
y = 3

Therefore, the solution to the system of equations is x = 7 and y = 3.
Answered by GPT 3.5
To solve this system of equations using the elimination method, we will first eliminate x by subtracting the second equation from the first equation.

(2x + 8y) - (2x - 4y) = 8 - (-16)
2x + 8y - 2x + 4y = 8 + 16
12y = 24
y = 24 / 12
y = 2

Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

2x + 8(2) = 8
2x + 16 = 8
2x = 8 - 16
2x = -8
x = -8 / 2
x = -4

Therefore, the solution to the system of equations is x = -4 and y = 2.
Answered by GPT 3.5
To solve this system of equations using the elimination method, we can add the two equations together to eliminate the variable x.

(7x + 3y) + (-7x + 9y) = -25 + (-47)
7x - 7x + 3y + 9y = -25 - 47
12y = -72
y = -72 / 12
y = -6

Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

7x + 3(-6) = -25
7x - 18 = -25
7x = -25 + 18
7x = -7
x = -7 / 7
x = -1

Therefore, the solution to the system of equations is x = -1 and y = -6.
Answered by GPT 3.5
To solve this system of equations using the elimination method, we will first multiply the first equation by 4 and the second equation by -1 to make the x terms cancel each other out when we add them.

4(-x + 6y) = 4(13)
-4x + 24y = 52

-1(4x - 10y) = -1(-10)
4x - 10y = 10

Now, we add the two equations:

(-4x + 24y) + (4x - 10y) = 52 + 10
14y = 62
y = 62 / 14
y = 31/7

Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:

-x + 6(31/7) = 13
-x + 186/7 = 13
-x = 13 - 186/7
-x = (91 - 186) / 7
-x = -95 / 7
x = 95 / 7

Therefore, the solution to the system of equations is x = 95/7 and y = 31/7.
Answered by GPT 3.5
The solution to the system of equations -x + 6y = 13 and 4x - 10y = -10 is (95/7, 31/7).
Answered by GPT 3.5
To get rid of the fractions, we can multiply both equations by 7 to eliminate the denominators:

Equation 1: -7x + 42y = 91
Equation 2: 28x - 70y = -70

Now, add the two equations together to eliminate x:

-7x + 42y + 28x - 70y = 91 - 70
21x - 28y = 21
3x - 4y = 3

Now we have two equations:
- x + 6y = 13
3x - 4y = 3

We can solve this new system of equations using the elimination method:

Multiply the first equation by 3 and the second equation by 1:

-3x + 18y = 39
3x - 4y = 3

Now, add the two equations together:

14y = 42
y = 3

Substitute y back into the first equation to solve for x:

-x + 6(3) = 13
-x + 18 = 13
-x = -5
x = 5

Therefore, the solution to the system of equations is x = 5 and y = 3, represented as (5, 3).