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

Selection of Quadratic Equations to Solve

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

Straightforward solving linear equations question.

Two questions on solving systems of simultaneous equations.

Straightforward solving linear equations question.

Adapted from 'Simultaneous equations by substitution 3 with parts' by Joshua Boddy.

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Two questions on solving systems of simultaneous equations.

Solve for $x$ and $y$:  \[ \begin{eqnarray} a_1x+b_1y&=&c_1\\   a_2x+b_2y&=&c_2 \end{eqnarray} \]

The included video describes a more direct method of solving when, for example, one of the equations gives a variable directly in terms of the other variable.

Solve for $x$: $\displaystyle \frac{a} {bx+c} + d= s$

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

Solving simple simultaneous equations.

Equations of type ax-b = c.

Includes advice.

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

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.

Finding values which satisfy an inequality.

Solving quadratic equations using the formula

Basic solving of linear equations

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

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

Two questions on solving systems of simultaneous equations.

Solve a pair of linear equations by writing an equivalent matrix equation.

Solve a pair of linear equations by writing an equivalent matrix equation.

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Solve a pair of linear equations by writing an equivalent matrix equation.

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