1 - Solving

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Simultaneous Equations

Section 1 Practise questions

Question 1

Given the linear simultaneous equations $$\quad\; x + 3y = 8 \qquad\qquad(1)$$ $$-x + 2y = 12 \qquad\qquad(2)$$ Solve for $x$ and $y$.

Add equations (1) and (2): $$5y = 20$$ $$\, y = 4$$ Substitute $y = 4$ into any of the equations: $$x + 3(4) = 8$$ $$\qquad\qquad x = -4$$

Question 2

Given the linear simultaneous equations $$\;\; 2x + y = -4 \qquad\qquad(1)$$ $$-x + 2y = 12 \qquad\qquad(2)$$ Solve for $x$ and $y$.

Multiply equation (2) by $2$: $$-2x + 4y = 24 \qquad\qquad(3)$$ Add equations (1) and (3): $$5y = 20$$ $$y = 4$$ Substitute $y = 4$ in equation (1) or equation (2): $$2x + 4 = -4$$ $$\qquad\; x = -4$$