System of Equations / Review

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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 algebraically?

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Solving a system of equations algebraically involves finding the values of the variables that satisfy all equations in the system using algebraic methods such as substitution or elimination.

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What is substitution in the context of solving equations?

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Substitution is a method where one equation is solved for one variable, and that expression is substituted into another equation.

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What is elimination in the context of solving equations?

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Elimination is a method where equations are manipulated to eliminate one variable, allowing for the solution of the remaining variable.

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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 infinite solutions?

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

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x = 9

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(3, 7)

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What is the first step to solve this system using substitution: 3x + 3y = 3, y = 3x + 5?

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We substitute 3x + 5 into the first equation and solve for x: 3x + 3(3x + 5) = 3.

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(3, -2)