Systems of Equations and Inequalities Review

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

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How do you solve a system of equations by graphing?

Back

To solve by graphing, plot each equation on the same coordinate plane and identify the point(s) where they intersect.

Front

What does it mean if a system of equations has no solution?

Back

It means the lines represented by the equations are parallel and never intersect.

Front

What is the elimination method for solving systems of equations?

Back

The elimination method involves adding or subtracting equations to eliminate one variable, making it easier to solve for the other.

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables. The solution is the region where the inequalities overlap.

Front

How do you graph a system of inequalities?

Back

Graph each inequality on the same coordinate plane, shading the region that satisfies each inequality.

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What does the symbol '≥' mean in inequalities?

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The symbol '≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the number.

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What is the substitution method for solving systems of equations?

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The substitution method involves solving one equation for one variable and substituting that expression into the other equation.

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What is the significance of the solution to a system of equations?

Back

The solution represents the values of the variables that satisfy all equations in the system simultaneously.

Front

What does it mean if a system of inequalities has no solution?

Back

It means there is no region where the inequalities overlap, indicating that the conditions cannot be satisfied simultaneously.