Question

Create an equivalent system of equations using the sum of the system and the first equation. x + 4y = 8 4x + y = 2

x + 4y = 8, 5x + y = 2
x + 4y = 8, 5x + 5y = 2
x + 4y = 8, 4x + 5y = 10
x + 4y = 8, 5x + 5y = 10

Answer 1

Option D

x + 4y = 8, 5x + 5y = 10

Explanation:

The first equation is given as x+4y=8

The sum of the system is x+4y=8 +(4x+y=2)

Adding like terms we obtain

5x+5y=10

Therefore, an equivalent system of equiations will be

x+4y=8, 5x+5y=10 hence option D

Answer 2

x + 4y = 8, 5x + 5y = 10

Explanation:

Given the next system of equation:

x + 4y = 8 (eq. 1)

4x + y = 2 (eq. 2)

We want an equivalent system of equations. If you add or subtract two equations, the solution of the system remains the same as the original. Also you can multiply or divide an equation by some coefficient and, again, the solution is not altered. So, adding eq. 1 to eq. 2:

x + 4y = 8

+

4x + y = 2

----------------

5x + 5y = 10 (eq. 3)

This new equation replace one equation of the original system. We are asked to create an equivalent system of equations using the sum of the system and the first equation, that is the next system:

x + 4y = 8 (eq. 1)

5x + 5y = 10 (eq. 3)

where eq. 3 replace eq. 2