AC9M8A02Year 8AlgebraPractised on site

AC9M8A02 — Year 8 Algebra

Official Curriculum Content Description:

graph linear relations on the Cartesian plane using digital tools where appropriate; solve linear equations and one-variable inequalities using graphical and algebraic techniques; verify solutions by substitution

Worked Examples (1)

Example 1Graphical Solution of Linear Equations
Solve the simultaneous linear system graphically by finding the coordinates of the point of intersection of the lines y=−3x+4y = -3x + 4 and y=−x−2y = -x - 2. Give your answer as an ordered pair (x,y)(x, y).
Common mistake: Transposing the coordinates as (y, x) instead of (x, y).
Correct Answer:(3,−5)(3, -5)
Worked Solution:
1. Equate the two linear expressions: −3x+4=−x−2-3x + 4 = -x - 2. 2. Solve for xx: (−3−(−1))x=−2−(4)  ⟹  −2x=−6  ⟹  x=3(-3 - (-1))x = -2 - (4) \implies -2x = -6 \implies x = 3. 3. Substitute x=3x = 3 into the first equation: y=−3(3)+4=−5y = -3(3) + 4 = -5. 4. The point of intersection is (3,−5)(3, -5).

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