Solving Systems of Equations (All Methods)

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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 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 remaining variable.

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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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How do you check the solution of a system of equations?

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To check the solution, substitute the values of the variables back into the original equations to see if they hold true.

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What is the graphical method of 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) where they intersect.

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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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Solve by elimination: 2x + 3y = 6 and 4x - 3y = 12.

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(3, 0) is the solution.

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Solve by substitution: y = 2x + 1 and 3x - y = 4.

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(1, 3) is the solution.