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 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 when substituted for the variables.

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What is the substitution method for solving systems of equations?

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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 for 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 remaining variable.

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What is the graphing method for solving systems of equations?

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The graphing method involves graphing each equation on the same coordinate plane and identifying the point(s) where they intersect.

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How do you determine if a point is a solution to a system of equations?

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Plug the x and y values of the point into each equation. If both equations are true, the point is a solution.

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What is the standard form of a linear equation?

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The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

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What does it mean for equations to be 'stacked' in the elimination method?

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'Stacked' means that the equations are written one above the other, aligning like terms vertically to facilitate elimination.

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Solve the system of equations using substitution: y = 2x + 3, x + y = 10.

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(x, y) = (2, 6).

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Solve the system of equations using elimination: 2x + 3y = 12, 4x - y = 5.

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(x, y) = (3, 0).