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.

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16-01-2020
Mathematics

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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 :

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Answer:

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

Step-by-step 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: [tex]y=2x[/tex]

Equation 2: [tex]y=-12x+5[/tex]

Substituting equation 1 in equation 2 to solve for [tex]x[/tex].

[tex]2x=-12x+5[/tex]

Adding [tex]12x[/tex] both sides.

[tex]2x+12x=-12x+12x+5[/tex]

[tex]14x=5[/tex]

Dividing both sides by 14.

[tex]\frac{14x}{14}=\frac{5}{14}[/tex]

[tex]x=\frac{5}{14}[/tex]

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

Since the [tex]x[/tex] for the solution is [tex]\neq 2[/tex], we can say that (2,4) is not a solution to the given system of equations.