Question

Here is a system of equations: y = 2xy = −12x + 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.

Answer 1

The point (2,4) is not a solution for the given system of equations.

Explanation:

In order to check if point (2,4) is a solution of the given system of equations, we will solve the given system algebraically to find the solutions.

Solving the system by substitution.

Equation 1:
`y=2x`

Equation 2:
`y=-12x+5`

Substituting equation 1 in equation 2 to solve for
`x`.

`2x=-12x+5`

Adding
`12x` both sides.

`2x+12x=-12x+12x+5`

`14x=5`

Dividing both sides by 14.

`(14x)/(14)=(5)/(14)`

`x=(5)/(14)`

To check the point (2,4) for the solution.

Since the
`x` for the solution is
`\\eq 2`, we can say that (2,4) is not a solution to the given system of equations.