Systems of Equations and Inequalities

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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 point to be a solution to a system of equations?

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A point is a solution to a system of equations if it satisfies all equations in the system.

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How do you determine if (0,0) is a solution to a system of equations?

Back

Substitute x=0 and y=0 into each equation. If all equations are true, then (0,0) is a solution.

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What is the substitution method in 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 elimination method in solving systems of equations?

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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 the graphical method for solving systems of equations?

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The graphical method involves graphing each equation on the same coordinate plane and identifying the point(s) of intersection.

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

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If two lines are parallel, the system has no solution because the lines never intersect.

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

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If two lines coincide, the system has infinitely many solutions because every point on the line is a solution.

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How do you combine equations to eliminate a variable?

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You can multiply one or both equations by a number to align coefficients, then add or subtract the equations to eliminate a variable.

Front

What is the first step in solving the system: y = 3 - x and 3y + x = 5?

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Substitute y = 3 - x into the second equation: 3(3 - x) + x = 5.