Question

find linear equation in 2 variables when eq 1 is 0.2x+0.3y=1.3 and eq 2 is 0.4x+0.5y=2.3 find x and y

Answer 1

AnswEr:-

❀ Your Answer Is:-

• x = 2.
• y = 3.

ExplanaTion:-

Given Equations:-

$\tt\longrightarrow0.2x + 0.3y = 1.3 ... \: \: eq(1). \\ \\ \tt\longrightarrow0.4x + 0.5y =2.3... \: \: eq(2).$

To Find:-

• The value of x.

So,

Lets multiply the whole eq(1) by 2:-

$\tt\longrightarrow2(0.2x + 0.3y = 1.3). \\ \\ \tt\longrightarrow0.4x + 0.6y = 2.6... \: eq(3).$

Now,

By subtracting eq(2) from eq(3) we get:-

$\tt\mapsto(0.4x + 0.6y) - (0.4x + 0.5y) = 2.6 - 2.3 \\ \\ \tt\mapsto \cancel{0.4x} \: + 0.6y \: \cancel{ - 0.4y} \: - 0.5y = 0.3 \\ \\ \rm(by \: \: ope n ing \: \: brackets) \\ \\ \tt\mapsto0.6y - 0.5y = 0.3 \\ \\ \tt\mapsto0.1y = 0.3 \\ \\ \tt\mapsto y = \frac{0 \cancel.3}{0 \cancel.1} \\ \\ \tt\mapsto y = \frac{3}{1} . \\ \\ \tt\mapsto y = 3.$

By putting the value of y in eq(1) we get:-

$\tt\mapsto0.2x + 0.3y = 1.3 \\ \\ \tt\mapsto0.2x + 0.3(3) = 1.3 \\ \\ \rm(by \: \: putti ing \: \: the \: \: value \: \: of \: \: y). \\ \\ \tt\mapsto0.2x + 0.9 = 1.3 \\ \\ \tt\mapsto0.2x = 1.3 - 0.9 \\ \\ \tt\mapsto0.2x = 0.4 \\ \\ \tt\mapsto x = \frac{0 \cancel.4}{0 \cancel.2} \\ \\ \tt\mapsto x = \cancel\frac{4}{2} . \\ \\ \tt\mapsto x = 2.$

❝$\tt\therefore$ The required value of x and y is 2 and 3 respectively.❞