Semester Exam Review-Solving 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 to solve a system of equations using substitution?

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To solve a system using substitution, you solve one equation for one variable and then substitute that expression into the other equation.

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What is the substitution method?

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The substitution method involves isolating one variable in one equation and substituting that expression into the other equation to find the values of the variables.

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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 two lines are parallel in a system of equations?

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

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What does it mean if two lines coincide in a system of equations?

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

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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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How do you represent a word problem as a system of equations?

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Identify the variables, translate the relationships and conditions into equations, and then form a system of equations.

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

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Coefficients determine the slope and position of the lines represented by the equations, affecting their intersection.