How many solutions of the system x - y = 3 and x^2 - y = 1 are there such that both x and y are real?
How many solutions of the system x - y = 3 and x^2 - y = 1 are there such that both x and y are real?
Let's rearrange the two equations
Rearrange x – y = 3 to y = x – 3
Rearrange x2 – y = 1 to y = x2 – 1
The answer to "How many..." is NONE.
I graphed both equations on Desmos. I tried to paste in a screenshot of the curves, but couldn't figure out how.
y = x2 – 1 is an upward opening parabola that crosses the y-axis at (0,–1)
y = x – 3 is a straight line that passes beneath the parabola and crosses the y-axis at (0,–3)
The two curves never intersect each other, so they have no solutions in common.
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