Elimination method

$$2x + y = 10 \quad \text{(Mlinganyo 1)}$$ $$x - y = 2 \quad \text{(Mlinganyo 2)}$$

Kumbuka kuwa coefficients za $y$ ni $+1$ na $-1$. Kwa kuongeza milinganyo, $y$ itaondolewa.

$$(2x + y) + (x - y) = 10 + 2$$ $$2x + y + x - y = 12$$ $$3x = 12$$

Gawanya pande zote mbili kwa 3.

$$\frac{3x}{3} = \frac{12}{3}$$ $$x = 4$$

Tutatumia Mlinganyo 2 ($x - y = 2$) kwa urahisi.

$$4 - y = 2$$

Toa 4 kutoka pande zote mbili.

$$-y = 2 - 4$$ $$-y = -2$$

Zidisha pande zote mbili kwa -1.

$$y = 2$$

Thamani za $x$ na $y$ ni 4 na 2 mtawalia.

Thamani ya $x$ ni: $\boxed{4}$
Thamani ya $y$ ni: $\boxed{2}$