Systems of Linear Equations
Lessons in this chapter
About Systems of Linear Equations
Systems of Linear Equations takes the system-solving skills from 8th grade and applies them at Algebra 1’s pace, with real modeling problems as the payoff.
Graphing Systems of Linear Equations finds a system's solution as the intersection point of two lines, while Algebraic Methods of Solving Systems of Linear Equations covers substitution and elimination for finding that same point without graphing.
Modelling using Systems of Linear Equations applies both methods to real two-unknown situations, translating a word problem into two equations and solving for where they agree.
This chapter is three lessons long and each one is an Algebra 1 worksheet worked in the page: Graphing Systems of Linear Equations, Algebraic Methods of Solving Systems of Linear Equations, and Modelling using Systems of Linear Equations. The questions are scored as you answer them, which is useful on the modeling set, where most of the difficulty is in choosing what each variable stands for before any algebra starts. Free to try, with no login needed for your first 3.
Frequently asked questions
Graphing Systems of Linear Equations finds the solution as the point where two lines cross, and shows the two cases where there is no such point or infinitely many. Algebraic Methods of Solving Systems of Linear Equations then solves the same systems exactly by substitution and elimination, and Modelling using Systems of Linear Equations turns a worded situation into two equations before solving it. The chapter sits in the high school Algebra conceptual category (A).
It means finding the one point (x, y) that makes both equations true at the same time: graphically, the point where both lines cross.
Solve one equation for one variable, substitute that expression into the other equation, solve the resulting one-variable equation, then use that value to find the other variable.
Add or subtract the two equations (after matching coefficients if needed) so one variable cancels out, leaving a one-variable equation to solve.
Substitution is usually faster when one equation is already solved for a variable (or very close to it); otherwise elimination is often quicker, especially when standard-form equations already have matching or easily matched coefficients.
The two equations describe parallel lines: same slope, different y-intercept, so they never intersect and there's no (x, y) that satisfies both.