Equations and inequalities

Question 1

How can simultaneous linear equations be solved by elimination?

Answer 1

Multiply one or both of the equations in such a way that there is either a common x value or a common y value. Then, if the signs of these values are the same, subtract one equation from the other, else add the equations. This will produce one equation with one unknown. One the value of this unknown has been found, it can be substituted back into one of the original equations, and then the other unknown solved for

Question 2

How can simultaneous linear equations be solved by substitution?

Answer 2

Rearrange one of the equations to make either x or y the subject. Then substitute this new equivalency into the unused equation, reducing it to having just one unknown. Solve for this unknown, and then substitute the solved value back into one of the original equations to solve for the other unknown

Question 3

How can simultaneous equations in which one equation is non-linear be solved?

Answer 3

Rearrange the linear equation to make either x or y the subject. Then substitute this new equivalency into the non-linear equation, reducing it to having just one unknown. Solve for the values of this unknown, and replace each value of the unknown into the linear equation to solve for the values of the other unknown

Question 4

What must be done when multiplying or dividing an inequality by a negative number?

Answer 4

The inequality sign must be flipped

Question 5

How may a quadratic inequality be solved?

Answer 5

Rearrange to give either ax²+bx+c>0 or ax²+bx+c<0. Then, if either a is positive and the quadratic expression is less than zero, or if a is negative and the quadratic expression is greater than zero, then the possible values will be in the range of the quadratic expression’s two roots. Else, the possible values will be any number not in this range