Equations which can be written in the form

\[\dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(y),   \dfrac{\mathrm{d}y}{\mathrm{d}x} = f(x)f(y)\]

can all be solved by integration.

In each case it is possible to separate the $x$'s to one side of the equation and the $y$'s to the other

Solving such equations is therefore known as solution by separation of variables

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

A variety of trigonometric equations which can be solved using inverse operations.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Rearranging simple equations to solve for x.

A (quadratic) function is skethed sketched. Three equations are given that can be solved using the graph. There is a chance there will only be one solution.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

This exercise will help you solve equations of type ax-b = c.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Solve $p - t < \text{or}> q$

This question takes the student through variety of examples of quadratic inequalities by asking them for the range(s) for which $x$ meets the inequality.

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Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Solving a system of three linear equations in 3 unknowns using Gauss Elimination in 4 stages. Solutions are all integral.

Solve $p - t < \text{or}> q$

Solve a quadratic equation by completing the square. The roots are not pretty!

Solve simple two step linear equations with feedback.

4 questions on using partial fractions to solve indefinite integrals.

4 questions on using partial fractions to solve indefinite integrals.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Solve for $x$: $\displaystyle ax ^ 2 + bx + c=0$.

Apply and combine logarithm laws in a given equation to find the value of $x$.

Solve for $x$: $\displaystyle 2\log_{a}(x+b)- \log_{a}(x+c)=d$. 

Make sure that your choice is a solution by substituting back into the equation.

Solve for $x$:  $\log_{a}(x+b)- \log_{a}(x+c)=d$

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve. 

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

This question tests the student's ability to solve simple linear equations by elimination. Part a) involves only having to manipulate one equation in order to solve, and part b) involves having to manipulate both equations in order to solve.