Simultaneous Equations Practice Questions

Solve the simultaneous equations

$$\frac{x}{4} + \frac{y}{3} = 2$$

$$2x - y = 5$$

You must show your working.

Write down the equation of the straight line that should be drawn to solve $x^2 - 3x - 4 = 0$.

Work out the equation of the straight line that should be drawn to solve $x^2 - 4x + 1 = 0$.

A rectangular flower bed has area $40\ \text{m}^2$ and perimeter $28\ \text{m}$.

The length of the flower bed is $x$ metres and the width is $y$ metres.

Use an algebraic method to work out the length and the width of the flower bed.

Solve the simultaneous equations

$$2x + y + z = 6$$

$$x - 2y + 3z = 13$$

$$3x + y - z = 2$$

Do not use trial and improvement.

You must show your working.

$$f(x) = 2x^3 + ax^2 + bx + 12$$

where $a$ and $b$ are constants.

It is given that $f(2) = 0$ and $f(-1) = 18$.

Work out the values of $a$ and $b$.

Solve the simultaneous equations

$$x^2 + y^2 = 10$$

$$x + 3y = 10$$

and state what your solution tells you about the line $x + 3y = 10$ and the circle $x^2 + y^2 = 10$.

Solve the simultaneous equations. Give your answers in their simplest form in terms of $k$.

Given also that $x = y$, work out the value of $k$.

The curve $y = ax^2 + bx + c$ passes through the three points

$$A(-1,\ 12) \qquad B(2,\ 3) \qquad C(4,\ 27)$$

Work out the values of $a$, $b$ and $c$.

Do not use trial and improvement.

You must show your working.