IGCSE Math B 3.I Linear and quadratic simultaneous equations Topic Practice

Solve the simultaneous equations
$$\begin{aligned}4x^2-y^2&=27\\x+2y&=3\end{aligned}$$
Show clear algebraic working.

$$\text{Solutions of } ax^2+bx+c=0 \text{ are } x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.$$

Solve the simultaneous equations
$$\begin{aligned} x^2+y^2&=26,\\ 2x+y&=9. \end{aligned}$$
Show clear algebraic working.

Solve the simultaneous equations
$$\begin{aligned}3x^2-\frac{10}{3}x+3&=2y\\2x+3y&=4\end{aligned}$$
Show clear algebraic working.

The diagram shows part of the curve $\mathbf C$ with equation $y=3x^2+16x-35$ and part of the line $\mathbf L$ with equation 2y-11x=110.
P and Q are the points of intersection of $\mathbf C$ and $\mathbf L$.
R is the point on the x-axis such that PR is parallel to the y-axis.
Show that the area of triangle PQR is $442.75\text{ cm}^2$.
You must show clear algebraic working.

Solve the simultaneous equations
$$\begin{aligned} 3x-4y&=25,\\ x^2+y^2&=26. \end{aligned}$$
Show clear algebraic working.

Figure 2 shows two shapes A and B.
All the lengths are in metres.

The corners of shape A are all right angles.
The area of shape A is $400 \mathrm{~m}^{2}$
Shape B is triangle PQR.
The perimeter of shape A is equal to the perimeter of shape B.

Find the value of x and the value of y.
Show clear algebraic working.

Solve the simultaneous equations
$$\begin{aligned}9-xy&=x^2\\4y-x&=11\end{aligned}$$
Show clear algebraic working.