SYSTEMS OF EQUATIONS in TWO VARIABLES
SYSTEMS OF EQUATIONS in TWO VARIABLES
A system of equations is a collection of two or more equations with the same set of unknowns. In solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system.
The equations in the system can be linear or non-linear. This tutorial
reviews systems of linear equations.
A problem can be expressed in narrative form or the problem can be expressed
in algebraic form.
Work the following problems. Click on Solution, if you want to
review the solutions.
Problem 2.1a:
A total of
$12,000 is invested in two funds paying 9%
and 11% simple interest. If the yearly interest is $1,180, how much of the
$12,000 is invested at 9% and how much is invested at 11%?
Solution
Problem 2.1b:
An airplane
flying into a headwind travels the 1800-mile
flying distance between two cities in 3 hours and 36 minutes. On the return
flight, the same distance is traveled in 3 hours. Find the ground speed of
the plane and the speed of the wind, assuming that both remain
constant.
Solution
Problem 2.1c:
Ten gallons of a 30% acid mixture is obtained
by mixing
a 20% solution with a 50% solution. How much of each must be used?
Solution
Problem 2.1d:
Five hundred tickets were sold for a certain music
concert. The tickets for the adults and children sold for $7.50 and $4.00,
respectively, and the total receipts for the performance were $3,312.50.
How many of each kind of ticket were sold?
Solution
Problem 2.1e:
Solve
for x and y in the following system of equations.
Problem 2.1f: Solve for x and y in the
following system of equations.
If you would like to return to the beginning of the two by two system of equations, click on Example.
If you would like to test yourself by working some problem similar to this example, click on
Problem.
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Author: Nancy Marcus
