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OhioMaths

Systems of Equations and Inequalities

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you graph a linear inequality in two variables, and how do you decide which side of the boundary line to shade and whether the line is solid or dashed?

Graph the solution set of a linear inequality in two variables as a half-plane, using a solid or dashed boundary and a test point to choose the shaded side (Ohio A-REI.12, A-REI.11).
An Ohio Algebra I answer on graphing a two-variable linear inequality (A-REI.12): drawing the boundary line solid or dashed, using a test point to pick the half-plane, and reading a half-plane as the solution set.
11 min answer →

How do you turn a word problem with two unknowns into a system of equations or inequalities, solve it, and interpret the answer in context?

Model situations with two unknowns using systems of equations or inequalities, solve them, and interpret the solution and constraints in context (Ohio A-CED.3, A-REI.6, A-REI.12).
An Ohio Algebra I answer on modeling with systems (A-CED.3): defining two variables, writing a system of equations or inequalities from a context, solving it, and interpreting the solution and feasible region.
12 min answer →

How do you solve a system of two linear equations exactly using substitution or elimination, and how do you tell when a system has one solution, no solution, or infinitely many?

Solve systems of two linear equations in two variables algebraically by substitution and by elimination, and identify systems with no solution or infinitely many solutions (Ohio A-REI.6, A-REI.5).
An Ohio Algebra I answer on solving linear systems algebraically (A-REI.6): the substitution method, the elimination method, when to pick each, and recognizing no-solution and infinitely-many-solution systems.
12 min answer →

How does the graph of a system of linear equations show its solution, and how do you read the solution as the point where the two lines cross?

Solve systems of two linear equations by graphing, reading the solution as the intersection point, and connect the graph to the algebraic outcome (Ohio A-REI.6, A-REI.11).
An Ohio Algebra I answer on solving linear systems by graphing (A-REI.6): graphing each line, reading the intersection as the solution, and what parallel and identical lines mean for the number of solutions.
11 min answer →

How do you graph a system of two linear inequalities, and how do you find the region of points that satisfy both at once?

Graph a system of linear inequalities in two variables and identify the solution as the overlap of the half-planes, including testing whether a point lies in the solution region (Ohio A-REI.12).
An Ohio Algebra I answer on systems of linear inequalities (A-REI.12): graphing each inequality, finding the overlapping region that satisfies both, and testing a point against every inequality in the system.
11 min answer →