Systems of Equations/Inequalities
Solve and Substitute (Substitution)
It's easy to solve an equation with one variable: you isolate the variable and find what number it is equal to. But, when you have equations with two variables, it can be impossible to find a single numerical value for either variable. However, if you have two equations, with the same variables, you can often solve for a variable in one equation and then substitute that answer into the other equation to solve. Remember, in math, you can always substitute variables, terms, and numbers for each other if they are equal.
Create Systems of Equations from Word Problems
Some word problems are best solved by creating a system of equations (or two equations that use the same variables).
How do you identify those word problems?
Word problems best solved with a system of equation usually give two different totals. One total is typically a straight sum (e.g., adult tickets plus kid tickets equal total tickets) and the other is a sum that uses a multiplier (e.g., adult tickets, which cost \$10, plus kid tickets, which cost \$6 equal sum total cost in dollars).
Systems of Equations (Elimination)
All linear equations graph as lines. A system of equations is more than one equation, so more than one line. The \"solution\" to that system of equations is where the lines cross.
Most lines intersect (or cross) once, so they have one solution, which is written as a coordinate. The solution of the system of lines graphed below is approximately (-3, -1)