Systems of equations

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What is a system of equations?

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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 to solve a system of equations?

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To solve a system of equations means to find the values of the variables that satisfy all equations in the system simultaneously.

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What are the three methods to solve a system of equations?

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1. Graphing 2. Substitution 3. Elimination

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What is the substitution method?

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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?

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

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

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A system has no solution if the equations represent parallel lines that never intersect.

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

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

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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 values of the point into each equation. If the equations are satisfied, the point is a solution.

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Solve the system: 2x + 3y = 6 and x - y = 1.

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(3, 0)

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Solve the system: 4x - y = 7 and 2x + y = 3.

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(2, -1)