Question

Solve the system of equations.
7x+3y=−25
−7x+9y=−47 (1 p

Answer 1

Solve the system of equations.
–x+6y=13
4x–10y=–10

Answer 2

Solve the system of equations.
3x+6y=21
–5x+2y=13

Answer 3

To solve the system of linear equations, we can use either the substitution method, the elimination method, or matrix methods. In this case, the elimination method seems straightforward because we can easily eliminate one of the variables by adding the two equations. Let's use that method:

The given system of equations is:
7x + 3y = -25 ... (1)
-7x + 9y = -47 ... (2)

Now, if we add equations (1) and (2), the term '7x' in equation (1) and '-7x' in equation (2) will cancel each other out. Here's how it would look when we add them together:

(7x + 3y) + (-7x + 9y) = -25 + (-47)
7x - 7x + 3y + 9y = -25 - 47
0 + 12y = -72
12y = -72

Now, we can solve for 'y' by dividing both sides of the equation by 12:

12y / 12 = -72 / 12
y = -6

Now that we have the value for 'y', we can substitute this value back into one of the original equations to find 'x'. Let's use equation (1) for this purpose:

7x + 3y = -25

Now replacing 'y' with '-6':
7x + 3(-6) = -25
7x - 18 = -25

We can now solve for 'x' by adding 18 to both sides:
7x = -25 + 18
7x = -7

Finally, divide both sides by 7 to isolate 'x':
x = -7 / 7
x = -1

The solution to the system of equations is (x, y) = (-1, -6).

Answer 4

To solve the system of linear equations, we can again use either substitution or elimination methods. Let's use the elimination method for this set of equations.

The given system of equations is:
-x + 6y = 13 ... (1)
4x - 10y = -10 ... (2)

To use the elimination method efficiently, we would like the coefficients of one of the variables to be the same or opposites so that we can eliminate that variable by addition or subtraction of the equations.

Let's make the coefficients of 'x' opposites so that the 'x' term cancels out when we add the equations together. We can do this by multiplying equation (1) by 4:

(4)(-x + 6y) = (4)(13)
-4x + 24y = 52 ... (3)

Now we have:
-4x + 24y = 52 ... (3)
4x - 10y = -10 ... (2)

We can add equation (3) and equation (2) together:

(-4x + 24y) + (4x - 10y) = 52 + (-10)
-4x + 4x + 24y - 10y = 52 - 10
0 + 14y = 42

Now we can solve for 'y':

14y = 42
y = 42 / 14
y = 3

With the value of 'y', we can now substitute it back into one of the original equations to solve for 'x'. Let's use equation (1):

-x + 6y = 13

Replace 'y' with '3':
-x + 6(3) = 13
-x + 18 = 13

Subtract 18 from both sides to solve for 'x':
-x = 13 - 18
-x = -5

Multiply both sides by -1 to isolate 'x':
x = 5

The solution to the system of equations is (x, y) = (5, 3).

Answer 5

To solve the system of linear equations, we can use either substitution or elimination methods. In this case, let's use the elimination method:

The given system of equations is:
3x + 6y = 21 ... (1)
-5x + 2y = 13 ... (2)

We need to manipulate the equations such that one of the variables gets eliminated when we add or subtract the equations. Looking at the coefficients, we can make the 'y' terms cancel by multiplying equation (1) by 2 and equation (2) by 6:

(2)(3x + 6y) = (2)(21) ... Multiply equation (1) by 2
(6)(-5x + 2y) = (6)(13) ... Multiply equation (2) by 6

We get:
6x + 12y = 42 ... (3)
-30x + 12y = 78 ... (4)

Now, let's subtract equation (4) from equation (3) to eliminate 'y':

(6x + 12y) - (-30x + 12y) = 42 - 78
6x + 12y + 30x - 12y = -36
36x = -36

Now we can solve for 'x':

36x = -36
x = -36 / 36
x = -1

With the value of 'x', we can now substitute it back into one of the original equations to solve for 'y'. Let's use equation (1):

3x + 6y = 21

Replace 'x' with '-1':
3(-1) + 6y = 21
-3 + 6y = 21

Add 3 to both sides to solve for 'y':
6y = 21 + 3
6y = 24

Divide both sides by 6 to get 'y':
y = 24 / 6
y = 4

The solution to the system of equations is (x, y) = (-1, 4).