What number of solutions would this system of equations have?𝑦=6𝑥+2y=6x+2−2𝑦=−12𝑥−4−2y=−12x−4
Question
What number of solutions would this system of equations have?𝑦=6𝑥+2y=6x+2−2𝑦=−12𝑥−4−2y=−12x−4
Solution
The system of equations is:
- y = 6x + 2
- -2y = -12x - 4
First, let's simplify the second equation by dividing every term by -2:
y = 6x + 2
Now, we can see that both equations are identical. Therefore, they represent the same line in the coordinate plane.
In this case, the system of equations has an infinite number of solutions, because every point on the line y = 6x + 2 is a solution.
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