Draw the graphs of the following equations: 2𝑥 − 𝑦 = 1 and 𝑥 + 2𝑦 = 13 Find the solutions of the equations from the graph and shade the triangular region formed by the lines and the 𝑌 − 𝑎𝑥𝑖𝑠.

We have been given a system of linear equations 2𝑥 − 𝑦 = 1 and 𝑥 + 2𝑦 = 13. 

We need to draw its graph. For, 2𝑥 − 𝑦 = 1 ⇒ 𝑦 = 2𝑥 − 1 

Putting 𝑥 = 0, 𝑤𝑒 𝑔𝑒𝑡 𝑦 =− 1 Putting 𝑥 = 1, 𝑤𝑒 𝑔𝑒𝑡 𝑦 = 1 

Putting 𝑥 = 2, 𝑤𝑒 𝑔𝑒𝑡 𝑦 = 3 We can draw its table as follows,

For, 𝑥 + 2𝑦 = 13 

⇒ 𝑦 = $\frac{13 - x}{2}$

Putting 𝑥 =− 1, 𝑤𝑒 𝑔𝑒𝑡 𝑦 = 7 

Putting 𝑥 = 3, 𝑤𝑒 𝑔𝑒𝑡 𝑦 = 5 

Putting 𝑥 = 5, 𝑤𝑒 𝑔𝑒𝑡 𝑦 = 4 

we can draw its table as follows,

We can plot its graph as

We can see that the two graphs intersect each other at a point (3, 5). Hence, the solution of the two equations is 𝑥 = 3 and 𝑦 = 5