Algebra - Unit 5 Review - Systems of Equations

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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What does it mean for a solution to satisfy a system of inequalities?

Back

A solution satisfies a system of inequalities if it makes all inequalities true when substituted into them.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≤ or ≥) or dashed line (for < or >). 2. Shade the region that satisfies the inequality.

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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 substituting that expression into the other equation.

Front

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.

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How do you determine if a system of equations has no solution?

Back

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

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What does it mean if a system of equations has infinite solutions?

Back

A system has infinite solutions if the equations represent the same line, meaning every point on the line is a solution.

Front

If a shirt costs $10 and a pair of shorts costs $10, how much would 7 shirts and 7 pairs of shorts cost?

Back

The total cost would be $140 (7 shirts x $10 + 7 shorts x $10).

Front

What is the graphical representation of the solution (3, 2) for the equations 2x - y = 4 and y = -2x + 8?

Back

The point (3, 2) is where the two lines intersect on a graph, representing the solution to the system.

Front

What is the first step in solving the system of equations 2x - y = 4 and y = -2x + 8?

Back

You can use substitution or elimination. For substitution, solve one equation for y and substitute into the other.