Question 1
Graphically, solve the following pair of equations
2x + y = 6 and 2x – y + 2 = 0
Find the ratio of the areas of the two triangles formed by the lines representing these equations with the X-axis and the lines with the y-axis.

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Solution

Given equation are 2x + y = 65 and 2x – y + 2 = 0
Table for equation 2x + y = 6
$\begin{matrix} X & 0 & 3 Y & 6 & 0 P o i n t s & B & A \end{matrix}$
Table for equation 2x – y + 2 = 0
$\begin{matrix} X & 0 & - 1 Y & 2 & 0 P o i n t s & D & C \end{matrix}$
Let $A_{1} a n d A_{2}$ represent the areas of $D e l t a A C E a n d Δ B D E$ , respectively

$N o w, A_{1} = A r e a o f Δ A C E = \frac{1}{2} \times A C \times P E = \frac{1}{2} \times 4 \times 4 = 8 a n d A_{2} = A r e a o f Δ B D E = \frac{1}{2} \times B D \times Q E = \frac{1}{2} \times 4 \times 1 = 2 ∴ A_{1} A_{2} = 8 : 2 = 4 : 1$
Hence, the pair of equations intersect graphically at point E (1, 4) i.e., x = 1 and y = 4

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