Systems of Equations and Inequalities Flashcard

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.

Front

How do you solve a system of equations graphically?

Back

To solve graphically, plot both equations on the same graph and identify the point(s) where they intersect.

Front

What does it mean for a point to be a solution to a system of equations?

Back

A point is a solution if it satisfies all equations in the system, meaning it makes all equations true when substituted.

Front

What is the substitution method for solving systems of equations?

Back

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

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 an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

Front

What does it mean if two lines are parallel in a system of equations?

Back

If two lines are parallel, they have no points of intersection, meaning the system has no solution.

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What does it mean if two lines are coincident in a system of equations?

Back

If two lines are coincident, they lie on top of each other, meaning there are infinitely many solutions.

Front

What is the point of intersection in a system of equations?

Back

The point of intersection is the solution to the system, representing the values of the variables that satisfy all equations.