Practice Problems - Systems of Linear Equations

X and Y Intercepts in Equation – from 5.1

What are the x and y intercepts of the equation 3y = 5x – 15?

Two Equations and Two Unknown in World Problem – Bank Accounts – from 5.2

You went on “Who Wants to Be a Millionaire” and won $500,000. You decide to put it all into the bank. There are two types of accounts: savings and utility. Savings account yield 6% interest annually, and utility accounts yield 10% interest annually. How much would you allocate to each account, if you want the annual interest income from savings account to be twice as much as your annual income from utility account?

Systems of Two Equations – from 5.2

Find the x and y coordinate of the intersection of the lines 3x – 2y = 11 and 5x + y = 1.

Two Equations and Two Unknown in Word Problem – Theater Admission – from 5.2

It costs $123 to send 6 children and 10 adults to the theatre. It costs $100 to send 10 children and 5 adults to the theatre. Assuming that the price for admission for each adult is the same, and the price for admission for each child is the same, what is the price of admission for one adult? All costs are admission costs. Hint: set up two equations with two unknowns.

Two Equation and Two Unknown in Word Problem – Muffin Shop – from 5.2

Stephen’s Muffin Shop produces and sells muffins each day. Each large muffin requires 2.0oz of dough and 2.5oz of bran, and each small muffin requires 1.0oz of dough and 1.5oz of bran, and that each day there are available 200oz of dough and 260oz of bran. How many muffins of each size need to be made each day to use up all the dough and bran he has available?

Systems of Three Equations With Row Reduction – from 5.3

Find the value of x, y, and z for the solution to the following system of equations:
3x + 9y + 6z = 15
0x + 2y + 4z = 2
1x + 3y + 1z = 5

Systems of Two Equations with Arbitrary Variables – from 5.3

Solve the following system of equation:
(if variable is arbitrary, set it equal to itself i.e. x=x)
x + 2y + z = 5
2x + 3y + 2z = 12