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 set of values that satisfy all equations simultaneously.

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What does it mean for a system of equations to have no solution?

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A system of equations has no solution when the equations represent parallel lines that never intersect.

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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 remaining variable.

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How do you determine if two lines are parallel?

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Two lines are parallel if they have the same slope but different y-intercepts.

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What is the graphical representation of a system of equations with one solution?

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The graphical representation shows two lines that intersect at a single point.

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What is the cost function for a pizza with toppings at Palanzio’s Pizzeria?

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The cost function is C = 6.80 + 0.90t, where C is the total cost and t is the number of toppings.

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What is the cost function for a pizza with toppings at Guido’s Pizza?

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The cost function is C = 7.30 + 0.65t, where C is the total cost and t is the number of toppings.

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The solution is x = 4 and y = -2.

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What does it mean if a system of equations has infinitely many solutions?

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It means that the equations represent the same line, and every point on that line is a solution.