Question

system of linear equations
6x+y=372
12x+4y=780
how would you enter this
information into the
ti36xpro

Explanation:

Step1: Enter Equation Mode

First, turn on the TI - 36X Pro. Press the "MODE" button. Scroll through the menu options until you find the "EQN" (Equation) mode. Select the "System" option for a system of linear equations. Then, choose the number of variables (in this case, 2 variables, \(x\) and \(y\)).

Step2: Enter Coefficients for First Equation

For the first equation \(6x + y=372\), the general form of a linear equation in two variables is \(a_1x + b_1y=c_1\). Here, \(a_1 = 6\), \(b_1 = 1\), and \(c_1=372\). Enter \(a_1 = 6\), \(b_1 = 1\), and \(c_1 = 372\) into the corresponding fields for the first equation.

Step3: Enter Coefficients for Second Equation

For the second equation \(12x + 4y = 780\), the general form is \(a_2x + b_2y=c_2\). Here, \(a_2=12\), \(b_2 = 4\), and \(c_2 = 780\). Enter \(a_2 = 12\), \(b_2=4\), and \(c_2 = 780\) into the corresponding fields for the second equation.

Step4: Solve the System

After entering all the coefficients, press the "SOLVE" button (usually labeled as "=" or a similar solve - related button). The calculator will then display the values of \(x\) and \(y\) that satisfy the system of linear equations.

If we were to solve it manually first (to check), we can use the elimination method. Multiply the first equation \(6x + y=372\) by 4 to get \(24x+4y = 1488\). Then subtract the second equation \(12x + 4y=780\) from this new equation:

\((24x + 4y)-(12x + 4y)=1488 - 780\)

\(24x+4y - 12x - 4y=708\)

\(12x=708\)

\(x = \frac{708}{12}=59\)

Substitute \(x = 59\) into the first equation \(6x + y=372\):

\(6\times59+y=372\)

\(354+y=372\)

\(y=372 - 354 = 18\)

But for the calculator entry, following the steps above will allow you to enter the system and solve it.

Answer:

To enter the system of linear equations \(6x + y = 372\) and \(12x+4y = 780\) into the TI - 36X Pro:

1. Enter "MODE" -> Select "EQN" -> Select "System" -> Select "2" (for 2 variables).
2. For the first equation (\(6x + y=372\)): Enter \(a_1 = 6\), \(b_1 = 1\), \(c_1 = 372\).
3. For the second equation (\(12x + 4y=780\)): Enter \(a_2 = 12\), \(b_2 = 4\), \(c_2 = 780\).
4. Press "SOLVE" to get the solution (\(x = 59\), \(y = 18\) when solved).