Question

Solve the following system of equations:

1. 6x - 2y = 20
2..2x + 4y = 16
Please enter your answers in the spaces provided and write the solution as an ordered pair (x, y).

Answer 1

(4, 2 )

Step-by-step explanation:

given the system of equations

6x - 2y = 20 → (1)

2x + 4y = 16 → (2)

multiplying (1) by 2 and adding the result to (2) will eliminate y

12x - 4y = 40 → (3)

add (2) and (3) term by term to eliminate y

(2x + 12x) + (4y - 4y) = 16 + 40

14x + 0 = 56

14x = 56 ( divide both sides by 14 )

x = 4

substitute x = 4 into either of the 2 original equations and solve for y

substituting into (2)

2(4) + 4y = 16

8 + 4y = 16 ( subtract 8 from both sides )

4y = 8 ( divide both sides by 4 )

y = 2

solution is (4, 2 )

Answer 2

To solve the given system of equations, we can use the elimination method. Multiplying the equations and adding them together helps eliminate one of the variables, allowing us to solve for the other variable. The solution to the system of equations is (61/39, -8/13).

Step-by-step explanation:

To solve the system of equations:

1. 6x - 2y = 20

2. 2x + 4y = 16

We can use the method of substitution or elimination. Let's use the elimination method.

Multiply equation 1 by 2 and equation 2 by -3 to eliminate the y terms:

1. 12x - 4y = 40

2. -6x - 12y = -48

Add these two equations to eliminate x:

13y = -8

Solve for y:

y = -8/13

Substitute this value back into equation 1 to solve for x:

6x - 2(-8/13) = 20

6x + 16/13 = 20

6x = 260/13 - 16/13

6x = 244/13

x = 244/78 or 61/39

Therefore, the solution to the system of equations is (61/39, -8/13).