Systems Reference Sheet

Algebra 1 · Axiom Academy

FORMULA SHEET Systems Reference Sheet Solution methods, solution types, and graphing rules for systems of linear equations and inequalities. Types of Solutions for Linear Systems Write both equations in slope-intercept form, y = mx + b . Graph both lines on the same coordinate plane. Identify the point of intersection — this point is the solution. Verify by substituting the (x, y) coordinates into both original equations. Solve one equation for one variable (e.g. isolate ). Substitute this expression into the other equation. Solve the resulting one-variable equation for its value. Back-substitute into an original equation to find the other variable. Write the solution as an ordered pair (x, y) and check. Write both equations in standard form, Ax + By = C . If needed, multiply one or both equations to create opposite coefficients for one variable. Add the equations to eliminate that variable. Solve the resulting one-variable equation. Graphing Systems of Linear Inequalities Steps to find the feasible region Graph the boundary line for each inequality using the rules above. Shade the solution region for each inequality. If unsure, test a point such as (0, 0) to see whether it satisfies the inequality. The solution to the system is the overlapping shaded area — the feasible region . For optimization problems, identify the coordinates of the vertices (corners) of the feasible region.

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