RevisionDojo

Exercises for Question Type 1: Solving for a given system of linear equations using technology - IB | RevisionDojo

Question 1

Use a calculator’s simultaneous equations solver to find $(x,y)$ that satisfy

\begin{aligned} 3x - 2y &= 7\\ 4x + y &= 18 \end{aligned}

[2]

Question 2

Use a calculator’s simultaneous equations solver to find $(x, y, z)$ that satisfy

\begin{aligned} 3x + y - z &= 7\\ 2x - 3y + 4z &= -1\\ x + 2y + 3z &= 12 \end{aligned}

[2]

Question 3

Use a calculator's simultaneous equations solver to determine whether the system has a solution. If so, find $(x,y,z)$ ; if not, state that there is no solution.

\begin{aligned} x - 2y + z &= -5 \\ 2x + y - 3z &= -4 \\ -3x + y + 2z &= 10 \end{aligned}

[2]

Question 4

Use a calculator’s simultaneous equations solver to find $(x,y)$ that satisfy

\begin{aligned} 0.3x + 1.2y &= 3.3\\ 1.5x - 0.9y &= 2.7 \end{aligned}

[2]

Question 5

The prices (in dollars) of an apple $a$ , a banana $b$ , and a cup of cherries $c$ satisfy the following conditions:

2 apples, 1 banana, and 1 cup of cherries cost $9
1 apple, 2 bananas, and 3 cups of cherries cost $14
3 apples, 1 banana, and 2 cups of cherries cost $13

Use a calculator’s simultaneous equations solver to find $(a,b,c)$ .

[3]

Question 6

Use a calculator’s simultaneous equations solver to find $(x,y,z)$ that satisfy

\begin{aligned} 3x + 2y - z &= 0\\ -x + 5y + 2z &= 1\\ 4x - y + 3z &= 21 \end{aligned}

[3]

Question 7

Use a calculator’s simultaneous equations solver to find $(x,y)$ that satisfy

\left\{ \begin{aligned} 2x + y &= 9 \\ x - y &= 3 \end{aligned} \right.

[2]

Question 8

Use a calculator’s simultaneous equations solver to find $(x, y, z)$ that satisfy

\begin{aligned} x + y + z &= 6 \\ 2x - y + 3z &= 9 \\ 3x + 4y - z &= 8 \end{aligned}

[3]

Question 9

Use a calculator’s simultaneous equations solver to find $(x,y,z)$ that satisfy

\begin{aligned} 1.5x + y - 2z &= 1\\ -x + 0.5y + z &= -2\\ 2x + 3y + 4z &= 3 \end{aligned}

[2]

Question 10

Find the intersection point of the lines $y=2x+1$ and $y=-x+10$ using a calculator’s simultaneous equations solver.

[2]

Question 11

A student buys 3 notebooks and 2 pens for $13, while another buys 2 notebooks and 5 pens for $16. Let $n$ be the price of a notebook and $p$ the price of a pen (in dollars). Use a calculator’s simultaneous equations solver to find $n$ and $p$ .

[4]

Question 12

Use a calculator’s simultaneous equations solver to find $(x,y,z)$ that satisfy

\begin{aligned} 0.5x + 0.5y + 0.5z &= 2 \\ 1.2x - 0.4y + 0.3z &= 3.7 \\ -0.7x + 0.2y + 0.5z &= -0.1 \end{aligned}

[3]

Question Type 1: Solving for a given system of linear equations using technology Exercises