Systems 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?

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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 graphical representation of a system of equations?

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The graphical representation of a system of equations is the intersection point(s) of the lines represented by the equations on a coordinate plane.

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

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A system of equations has no solution if the lines represented by the equations are parallel and 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 of equations 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 the solution of a system of equations graphically?

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To determine the solution graphically, plot the equations on a coordinate plane and identify the point(s) where the lines intersect.

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What is the point of intersection in a system of equations?

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The point of intersection is the coordinate point (x, y) that satisfies all equations in the system.

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What is a consistent system of equations?

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A consistent system of equations is one that has at least one solution, meaning the lines intersect at one or more points.