Question

Claire completed the steps to solve the system of equations.

Answer 1

Option D:

No, Claire should have gotten –2y = –8 instead of 2y = –8 in step 4.

Solution:

The system of equations are

4x – 2y = 4 – – – – (1)

3x + 3y = 21 – – – – (2)

Step 1: Multiply the equation (1) by 3 and equation (2) by 2

12x – 6y = 12

6x + 6y = 42

Step 2: Add the above equations.

`\begin{aligned}&12 x-6 y=12\\&6 x \ +\ 6 y\ =42\\&-------\\&18x\ \ =\ 54\end{aligned}`

⇒ 18x = 54

Step 3: Divide both sides of the equation by 18.

⇒ x = 3

Step 4: Substitute x = 3 in equation (1)

4(3) – 2y = 4

⇒ 12 – 2y = 4

Subtract 12 from both sides of the equation.

⇒ –2y = –8

Divide by –2 on both sides of the equation.

⇒ y = 4

Step 5: The solution is (3, 4).

But Claire's solution is (3, –4).

Claire's solution is not correct in step 4.

Option D is the correct answer.

No, Claire should have gotten –2y = –8 instead of 2y = –8 in step 4.