ask 1 part A

Two Mathematics students Piripi and Riana who had just completed learning about linear systems at school were experimenting with the equations. They wrote down two equations and to investigate the systems further they included an unknown coefficient in one of the equations.

Equation 1: 3x + y 2z = 7

Equation 2: az = x + y + 6

To form the third equation they asked their friend Fatima to suggest a 4 digit number. Fatima came up with the number 2219. The digits 2, 2, 1, 9 will be the coefficients of x, y, z and the constant term in that order, given that the equation is in the form: ax + by + cz = d.

Write down Equation 3 and solve the set of three equations when a = 3.

Find the values of a, for which the system is consistent. Give algebraic reasons for your answer and interpret the solution geometrically. Piripi and Riana wanted to experiment with the equations still further continuing to use a = 3. Investigate the solutions to the set of equations described in the two situations given below. Give a geometric interpretation of the solution for each set of equations and describe the solution for each set.

Task 2 part A

New set of three equations is formed using the original Equation 1 and Equation 2 and the third equation is formed by multiplying all the coefficients and the constant in Equation 1 by 3.

Part B

A new set of three equations is formed using the original Equation 1 and Equation 2 and the third equation is formed by using Equation 1 with the constant changed from -7 to 12

Task 3

Tyrone inherited $25,000 and invested part of it in a money market account, part in bonus bonds and part in a mutual fund. After one year, he received a total of $1,620 in simple interest from the three investments. The money market paid 6% annually, the bonds paid 7% annually, and the mutual fund paid 8% annually. There was $6000 more invested in the bonds than the mutual funds.

Set up and solve a system of equations to find the amount Tyrone invested in each category.