Solve graphically the simultaneous equations 3x−2y=5 and 5x+y=17

Kwa mlinganyo wa kwanza, $3x - 2y = 5$:
Tengeneza $y$ kuwa mada ya fomula: $2y = 3x - 5 \implies y = \frac{3x - 5}{2}$

• Wakati $x = 1$: $y = \frac{3(1) - 5}{2} = \frac{-2}{2} = -1$. Pointi ni $(1, -1)$.
• Wakati $x = 3$: $y = \frac{3(3) - 5}{2} = \frac{9 - 5}{2} = \frac{4}{2} = 2$. Pointi ni $(3, 2)$.
• Wakati $x = 5$: $y = \frac{3(5) - 5}{2} = \frac{15 - 5}{2} = \frac{10}{2} = 5$. Pointi ni $(5, 5)$.

Kwa mlinganyo wa pili, $5x + y = 17$:
Tengeneza $y$ kuwa mada ya fomula: $y = 17 - 5x$

• Wakati $x = 2$: $y = 17 - 5(2) = 17 - 10 = 7$. Pointi ni $(2, 7)$.
• Wakati $x = 3$: $y = 17 - 5(3) = 17 - 15 = 2$. Pointi ni $(3, 2)$.
• Wakati $x = 4$: $y = 17 - 5(4) = 17 - 20 = -3$. Pointi ni $(4, -3)$.

Chora mfumo wa kuratibu wa Cartesian (x-axis na y-axis).

• Panga pointi $(1, -1)$, $(3, 2)$, na $(5, 5)$ kwa mlinganyo wa kwanza na chora mstari unaopita kati yake.
• Panga pointi $(2, 7)$, $(3, 2)$, na $(4, -3)$ kwa mlinganyo wa pili na chora mstari unaopita kati yake.

Ukiangalia pointi tulizopata, utaona kwamba pointi $(3, 2)$ inapatikana katika orodha zote mbili. Hii inamaanisha kuwa mistari miwili itakutana kwenye pointi hii.

Suluhisho la milinganyo hii ni sehemu ya makutano ya mistari miwili, ambayo ni:

$$x = 3, y = 2$$