Here is a system of equations y= 2x y= -1/2x + 5 determine whether (2,4) is a solution to this system use algebra to show whether (2,4) is or is not a solution to the system. show all work and explain each step.

(2,4) is a solution to this system

Step-by-step explanation:

The given system of equations is expressed as

y = 2x - - - - - - - - - - - 1

y = -1/2x + 5 - - - - - - - - - 2

The first step is to equate equation 1 to equation 2. It becomes

2x = - 1/2x + 5

The next step is to add - 1/2x to the left hand side and the right hand side of the equation. It becomes

2x + x/2 = - x/2 + x/2 + 5

(4x + 2)/2 = 5

The next step is to multiply the left hand side and the right hand side of the equation by 2. It becomes

(4x + 2)/2 × 2= 5 × 2

4x + 2 = 10

Subtracting 2 from the left hand side and the right hand side of the equation. It becomes

4x + 2 - 2 = 10 - 2

4x = 8

Dividing the left hand side and the right hand side of the equation by 4, It becomes

4x/4 = 8/4

x = 8/4 = 2

Substituting x = 2 into equation 1, it becomes

y = 2 × 2 = 4

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0