Question

Use the substitution method to solve the system of equations. Choose the correct ordered pair. 14x - 2y = 78 2x - 2y = 6

Answer 1

Answer:

(6 , 3)

Solution,

$14x - 2y = 78 \\ or \: 14x = 78 + 2y \\ x = \frac{78 + 2y}{14} ..........equation \: (i)$

$\\ \\ 2x - 2y = 6$

Putting the value of x from equation (i)

$2 \times \frac{78 + 2y}{14} - 2y = 6 \\ or \: \frac{78 + 2y}{7} - 2y = 6 \\ or \: \frac{78 + 2y - 2y \times 7}{7} = 6 \\ or \: \frac{78 + 2y - 14y}{7} = 6 \\ or \: \frac{78 - 12y}{7} = 6 \\ or \: 78 - 12y = 6 \times 7 \\ or \: 78 - 12y = 42 \\ or \: - 12y = 42 - 78 \\ or \: - 12y = - 36 \\ or \: y = \frac{ - 36}{ - 12} \\ y = 3$

Now, putting the value of y in equation (i)

$x = \frac{78 + 2y}{14} \\ = \frac{78 + 2 \times 3}{14} \\ = \frac{78 + 6}{14} \\ = \frac{84}{14} \\ = 6$

Value of X is 6

Value of y is 3

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Answer 2

Answer:

(6, 3)

Step-by-step explanation:

Step 1: Rearrange 2nd equation

2x = 2y + 6

x = y + 3

Step 2: Substitution

14(y + 3) - 2y = 78

14y + 42 - 2y = 78

12y + 42 = 78

12y = 36

y = 3

Step 3: Plug in y to find x

2x - 2(3) = 6

2x - 6 = 6

2x = 12

x = 6