Exercises for Question Type 2: Finding the intersection points between two different lines

Question 1

Skill question

Find the intersection of the lines $y = - 3 x + 7$ and $y = 2 x - 5$ .

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Question 2

Skill question

Solve for the intersection of $y = 0.5 x - 2$ and $x - y = 6$ .

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Question 3

Skill question

Calculate the intersection of the lines $x + y = 4$ and $2 x + 2 y = 10$ .

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Question 4

Skill question

Find the point where the lines $\frac{x}{2} + \frac{y}{3} = 1$ and $y = - 2 x + 4$ intersect.

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Question 5

Skill question

Determine the intersection point of the line $4 x - 2 y = 8$ with the line $y = x + 1$ .

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Question 6

Skill question

Determine the intersection of the line $y = 3 x - 4$ and the perpendicular line through $(3, 4)$ .

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Question 7

Skill question

The equations of two roads are given as linear functions of $x$ . The intersection point $(x, y)$ represents where the two roads meet.

Two roads are modeled by $y = 0.8 x + 5$ and $y = - 1.2 x + 20$ . At what point do they meet?

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Question 8

Skill question

A supplier’s cost is $C_{1} (x) = 50 x + 200$ and a competitor’s is $C_{2} (x) = 30 x + 500$ . At what production level $x$ are the costs equal?

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Question 9

Skill question

The problem requires finding the intersection point of two lines, each defined by two given coordinates. Students must calculate the gradient, determine the equation for each line, and then solve the resulting system of linear equations.

Find the intersection point of the line passing through $(1, 2)$ and $(3, 6)$ and the line passing through $(- 2, 8)$ and $(4, - 2)$ .

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Question 10

Skill question

Calculate the intersection point of the lines $y = 5 x + 4$ and $y = 2 x - 3$ .

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Question 11

Skill question

Find the intersection point of $3 x + 4 y = 12$ and $5 x - 2 y = 7$ .

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IB Mathematics Applications & Interpretation Question Type 2: Finding the Intersection Points Between Two Different Lines Exercises