Solve the system of equations.

Question

6x - 5y = 27
3x + 5y = 36
(_,_)

Answer 1

To solve this system of equations, we can add the two equations together to eliminate the y variable.

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

Now that we have found the value of x, we can substitute it back into one of the original equations to solve for y.

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

Therefore, the solution to the system of equations is (7, 3).

Answer 2

Solve the system of equations.
2x + 8y = 8
2x - 4y = -16
(_,_)

Answer 3

To solve this system of equations, we can use the elimination method by subtracting the second equation from the first equation to eliminate the x variable.

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

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

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

Therefore, the solution to the system of equations is (-4, 2).

Answer 4

Solve the system of equations.
7x + 3y = -25
-7x + 9y = -47
(_,_)

Answer 5

To solve this system of equations, we can use the elimination method by adding the two equations together to eliminate the x variable.

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

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

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

Therefore, the solution to the system of equations is (-1, -6).

Answer 6

Solve the system of equations.
-x + 6y = 13
4x - 10y = -10
(_,_)

Answer 7

To solve this system of equations, we can use the elimination method by first multiplying the first equation by 4 to match the coefficient of x in the second equation.

1) -4x + 24y = 52
2) 4x - 10y = -10

Now, we can add these two equations together to eliminate the x variable:

-4x + 24y + 4x - 10y = 52 - 10
14y = 42
y = 3

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

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

Therefore, the solution to the system of equations is (5, 3).

Answer 8

Solve the system of equations.
3x + 6y = 21
-5x + 2y = 13
(_,_)

Answer 9

To solve the system of equations, we can use the elimination method. Let's multiply the first equation by 5 and the second equation by 3 to make the coefficients of y equal.

1) 15x + 30y = 105
2) -15x + 6y = 39

Now, we can add these two equations together to eliminate the x variable:

15x + 30y - 15x + 6y = 105 + 39
36y = 144
y = 4

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

3x + 6(4) = 21
3x + 24 = 21
3x = -3
x = -1

Therefore, the solution to the system of equations is (-1, 4).