Systems of Equations
Interactive practice questions
Consider the hyperbola $y=\frac{3}{x}$y=3x and the line $y=5$y=5.
a
To solve for the point of intersection of the hyperbola and the line, Laura forms the equation $\frac{3}{x}=5$3x=5. At how many points will the two graphs intersect?
b
Solve for the $x$x-coordinate of the point of intersection.
c
Hence state the coordinates of the point of intersection in the form $\left(x,y\right)$(x,y).
Easy
3min
Consider the hyperbola $xy=2$xy=2 and the straight line $y=x+6$y=x+6.
Easy
1min
Consider the circle with equation $x^2+y^2=22$x2+y2=22 and the line with equation $y=2$y=2.
Easy
5min
The parabola $y=x^2+1$y=x2+1 has been graphed on the number plane.
State the minimum value of $k$k such that the line $y=k$y=k has at least one point of intersection with the parabola.
Medium
< 1min
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