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 for an ordered pair to be a solution of a system of equations?

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An ordered pair (x, y) is a solution of a system of equations if it satisfies all equations in the system when substituted for x and y.

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How can you determine if an ordered pair is a solution to a system of equations?

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Substitute the x and y values of the ordered pair into each equation. If both equations are true, then the ordered pair 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 then 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) where the graphs intersect.

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What does it mean if two lines are parallel in the context of systems of equations?

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If two lines are parallel, it means they have no points of intersection, indicating that the system of equations has no solution.

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What does it mean if two lines coincide in the context of systems of equations?

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If two lines coincide, they lie on top of each other, indicating that there are infinitely many solutions to the system of equations.

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How do you solve the system of equations: x + 2y = -3 and x - y = -12?

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Using substitution or elimination, the solution is (-9, 3).

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What is the solution to the system of equations: y = 3x - 8 and y = 4 - x?

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The solution is the point where the two lines intersect, which is (3, 1).