Algebra 1 Unit 6 Test Review

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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 set of all points that satisfy all inequalities in the system.

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How do you graph a system of inequalities?

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To graph a system of inequalities, first graph each inequality as if it were an equation. Then, shade the region that satisfies the inequality. The solution set is where the shaded regions overlap.

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

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A system of equations has no solution if the graphs of the equations are parallel lines, meaning they never intersect.

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What is the substitution method in solving systems of equations?

Back

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

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What is the elimination method in 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 variable.

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What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

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What is the slope of a line?

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The slope of a line is a measure of its steepness, calculated as the rise over run (change in y over change in x). It indicates how much y changes for a given change in x.

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What is the y-intercept of a line?

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The y-intercept is the point where the line crosses the y-axis. It is the value of y when x = 0.

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How do you determine if a point is a solution to a system of equations?

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To determine if a point is a solution, substitute the x and y values of the point into each equation. If the point satisfies all equations, it is a solution.

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What is a consistent system of equations?

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A consistent system of equations has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).