Question

The table can be used to determine the solution of equations, 2x - 2y = 6 and 4x + 4y = 28.

Answer 1

Answer:

(5, 2)

Step-by-step explanation:

Given the following system of equations;

2x - 2y = 6  ......equation 1.

4x + 4y = 28  ......equation 2.

To get an equivalent equation, we would multiply eqn 1 by 2;

2 * (2x - 2y = 6) = 4x - 4y = 12

The new equivalent system of equations are;

4x - 4y = 12

4x + 4y = 28  

Adding the equivalent system of equations, we have;

(4x + 4x) + (-4y + 4y) = (12 + 28)

8x + 0 = 40

8x = 40

x = 40/8

x = 5

Next, we would find the value of y;

2x - 2y = 6

Substituting the value of x, we have;

2(5) - 2y = 6

10 - 2y = 6

Rearranging the equation (collecting like terms), we have;

2y = 10 - 6

2y = 4

y = 4/2

y = 2

Therefore, the solutions to the new system of equations are 5 and 2.

Check:

2x - 2y = 6

Substituting the values, we have;

2(5) - 2(2) = 6

10 - 4 = 6

6 = 6