New Zealand
Level 7 - NCEA Level 2

# Systems of Linear and Non-Linear Functions

## 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
Approx 3 minutes

Consider the hyperbola $xy=2$xy=2 and the straight line $y=x+6$y=x+6.

Consider the circle with equation $x^2+y^2=22$x2+y2=22 and the line with equation $y=2$y=2.

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.

### Outcomes

#### M7-8

Form and use pairs of simultaneous equations, one of which may be non-linear

#### 91269

Apply systems of equations in solving problems