Algebra 2

Section 1Simultaneous equations

Simultaneous equations are two or more equations solved together. The solution is the value pair that makes both equations true. For two straight lines, this solution is the point where the lines meet.

Section 2Elimination

Elimination solves simultaneous equations by adding or subtracting equations to remove one variable. Match the coefficients of one variable first, then eliminate it. Watch out: if signs are the same, subtract; if signs are different, add.

Section 3Substitution

Substitution solves simultaneous equations by writing one variable in terms of another, then replacing it in the second equation. This is handy when one equation already says something like y = 2x + 1. Here's the trick: substitute into the other equation, not back into the same one.

Section 4Quadratic expressions

A quadratic expression has a highest power of 2, such as x^2 + 5x + 6. Many quadratics can be factorised into two brackets. In plain words, you are looking for two numbers that multiply to the constant term and add to the middle coefficient.

Section 5Solving quadratic equations

A quadratic equation can have two solutions, one solution, or no real solutions. When a product equals zero, at least one factor must be zero. So if (x - 3)(x + 2) = 0, then x = 3 or x = -2.

Section 6Quadratic inequalities

Quadratic inequalities compare a quadratic expression with zero using signs like <, >, <=, or >=. First find the roots, then test intervals or use the shape of the parabola. Easy to mix up - the answer is often a range of values, not just the roots.

Section 7Checking answers

Substitute answers back into the original equations, especially for simultaneous equations. In exam-style algebra, a quick check catches sign errors. For a shop problem in Jamaica, if x is the number of items, a negative answer may signal that you made an algebra mistake or that the model does not fit the context.