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

Question 1

Skill question

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

$3 x - 2 y 4 x + y = 7 = 18$

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Question 2

Skill question

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

$3 x + y - z 2 x - 3 y + 4 z x + 2 y + 3 z = 7 = - 1 = 12$

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Question 3

Skill question

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.

$x - 2 y + z 2 x + y - 3 z - 3 x + y + 2 z = - 5 = - 4 = 10$

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Question 4

Skill question

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

$0.3 x + 1.2 y 1.5 x - 0.9 y = 3.3 = 2.7$

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Question 5

Skill question

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

Skill question

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

$3 x + 2 y - z - x + 5 y + 2 z 4 x - y + 3 z = 0 = 1 = 21$

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Question 7

Skill question

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

${2 x + y x - y = 9 = 3$

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Question 8

Skill question

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

$x + y + z 2 x - y + 3 z 3 x + 4 y - z = 6 = 9 = 8$

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Question 9

Skill question

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

$1.5 x + y - 2 z - x + 0.5 y + z 2 x + 3 y + 4 z = 1 = - 2 = 3$

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Question 10

Skill question

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

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Question 11

Skill question

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

Skill question

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

$0.5 x + 0.5 y + 0.5 z 1.2 x - 0.4 y + 0.3 z - 0.7 x + 0.2 y + 0.5 z = 2 = 3.7 = - 0.1$

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IB Mathematics Applications & Interpretation Question Type 1: Solving for a Given System of Linear Equations Using Technology Exercises