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 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 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 they intersect.

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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 an inconsistent system of equations?

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An inconsistent system has no solution because the equations represent parallel lines that never intersect.

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What is a dependent system of equations?

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A dependent system has infinitely many solutions because the equations represent the same line.

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What is an independent system of equations?

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An independent system has exactly one solution, where the lines intersect at a single point.

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Solve the system of equations: 5x + 3y = 7 and y = 4.

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(-1, 4)