Question

The solution to the system of equations shown is (2,0).
3x – 2y = 6
x + 4y = 2
When the first equation is multiplied by 2, the sum of the two
equations is equivalent to 7x = 14

Which system of equations will also have a solution of (2,0)?

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

The system of equation will also have a solution of (2,0) are,

x + 4y = 2, 7x = 14.

Given that,

The solution to the system of equations shown is (2,0).

3x – 2y = 6 ,  x + 4y = 2

When the first equation is multiplied by 2, the sum of the two  equations is equivalent to 7x = 14.

We have to determine,

Which system of equations will also have a solution of (2,0).

According to the question,

To determine the system of the equation after applying all the given conditions in the steps, follow all the steps given below.

System of equations;  3x – 2y = 6 ,  x + 4y = 2.

• Step1; Multiply the first equation by 2,

                   $2 \times (3x-2y) = 2 \times 6\\\\6x - 4y = 12$

• Step2; Adding equation 1 after multiplying by 2 from equation 2.

                   $6x - 4y + x + 4y = 12+ 2\\\\7x = 14\\\\x = \dfrac{14}{7}\\\\x = 2$

   

• Step3;  When x = 2 the value of y is,

                      $6(2) - 4y = 6\\\\12-4y = 6\\\\-4y = 6-12\\\\-4y == -6\\\\y = \dfrac{-6}{-4}\\\\y = \dfrac{3}{2}$

Hence, The required system of equation will also have a solution of (2,0) are, x + 4y = 2, 7x = 14.

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