Systems of Equations Review

Front

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

Back

The two lines represented by the equations are the same line.

Front

What are the equations representing the number of adult tickets (a) and children tickets (c) sold if a group of 11 people costs $228?

Back

a + c = 11 and 22a + 15c = 228.

Front

Which system of equations can be used to find the number of dimes (d) and nickels (n) if there are 80 coins totaling $6.60?

Back

d + n = 80 and 0.10d + 0.05n = 6.60.

Front

How many apples and oranges were sold if the total sales were $35 from 15 fruits, with apples costing $2 and oranges $3?

Back

5 apples and 10 oranges were sold.

Front

What system of equations can be used to find the price of senior (c) and student (s) tickets sold for $102 and $126?

Back

4c + 5s = 102 and 7c + 5s = 126.

Front

What is a system of equations?

Back

A set of two or more equations with the same variables.

Front

What does it mean for two lines to be parallel in the context of systems of equations?

Back

They have no solutions because they never intersect.

Front

How can you determine if a system of equations has a unique solution?

Back

If the lines represented by the equations intersect at exactly one point.

Front

What is the graphical representation of a system of equations?

Back

It is represented by the intersection points of the lines on a coordinate plane.

Front

What is the substitution method in solving systems of equations?

Back

It involves solving one equation for one variable and substituting that value into the other equation.