Solve the system of equations by elimination. Identify the correct solution below. 7x+2y=67𝑥+2𝑦=6−14x−4y=−12−14𝑥−4𝑦=−12Question 3Select one:a.No solutionb.Infinite number of solutionsc.(7, 2)d.(6,-12)
Question
Solve the system of equations by elimination. Identify the correct solution below. 7x+2y=67𝑥+2𝑦=6−14x−4y=−12−14𝑥−4𝑦=−12Question 3Select one:a.No solutionb.Infinite number of solutionsc.(7, 2)d.(6,-12)
Solution
The system of equations is:
- 7x + 2y = 6
- -14x - 4y = -12
First, we can simplify the second equation by dividing every term by -2:
7x + 2y = 6
Next, we subtract the second equation from the first:
(7x + 2y) - (7x + 2y) = 6 - 6
This simplifies to:
0 = 0
This means that the two equations are dependent and identical, so they represent the same line. Therefore, there are an infinite number of solutions that satisfy both equations.
So, the correct answer is:
b. Infinite number of solutions
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