Systems of Equations mixed review

Front

What is a system of equations?

Back

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 in the system.

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

Back

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

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you determine if a system of equations has one solution, no solution, or infinitely many solutions?

Back

If the lines intersect at one point, there is one solution. If the lines are parallel, there is no solution. If the lines coincide, there are infinitely many solutions.

Front

What is the graphical representation of a system of equations?

Back

The graphical representation of a system of equations is the intersection of the lines represented by each equation on a coordinate plane.

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What is the first step in solving the system -3x - 3y = 3 and y = -5x - 17 using substitution?

Back

The first step is to substitute y from the second equation into the first equation: -3x - 3(-5x - 17) = 3.

Front

What is the cost equation for a large pizza at Palanzio’s Pizzeria with x toppings?

Back

The cost equation is y = 6.80 + 0.90x, where y is the total cost.

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What is the cost equation for a large cheese pizza at Guido’s Pizza with x toppings?

Back

The cost equation is y = 7.30 + 0.65x, where y is the total cost.

Front

How can you find the number of toppings when both pizza companies cost the same?

Back

Set the two cost equations equal to each other: 6.80 + 0.90x = 7.30 + 0.65x and solve for x.

Front

What does it mean for two equations to be equivalent?

Back

Two equations are equivalent if they have the same solution set, meaning they represent the same line in a graph.