GMAS Review - Systems of Equations

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What is a system of linear equations?

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A system of linear equations is a set of two or more linear equations with the same variables. The solution is the point(s) where the equations intersect on a graph.

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What does it mean to solve a system of equations graphically?

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Solving a system of equations graphically means plotting the equations on a graph and identifying the point(s) where they intersect, which represents the solution.

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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 remaining 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 representing 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 using substitution?

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To use substitution, solve one equation for one variable and substitute that expression into the other equation to find the value of the second variable.

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What is the graphical representation of the solution (3, 0) for a system of equations?

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The point (3, 0) is where the two lines representing the equations intersect on a graph.

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How do you check if a solution is correct for a system of equations?

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To check if a solution is correct, substitute the values of the solution into both equations. If both equations are satisfied, the solution is correct.

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What is the significance of the coefficients in a system of equations?

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The coefficients in a system of equations determine the slope and position of the lines on a graph, affecting the number of solutions.

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The first step is to align the equations and manipulate them to eliminate one variable, often by multiplying one or both equations.