Question

12. Solve the given pair of linear equations by cross multiplication method: 8x + 5y =9; 3x + 2y =4
OR​

Answer 1

Answer:

x = -2 and y = 5

Step-by-step explanation:

Given Equations are,

8x + 5y = 9

8x + 5y - 9 = 0 ....................(1)

3x + 2y = 4

3x + 2y - 4 = 0 .......................(2)

here,

a1=8. b1=5. c1=-9. a2=3. b2=2 and c_2=-4

since, \frac{a_1}{a_2}\neq\frac{a_2}{b_2}

There exist unique solution,

By cross multiplication method we get,

\frac{x}{5\times(-4)-2\times(-9)}=\frac{y}{-9\times3-(-4)\times8}=\frac{1}{8\times2-3\times5}

First Consider,

\frac{x}{5\times(-4)-2\times(-9)}=\frac{1}{8\times2-3\times5}

\frac{x}{-2}=\frac{1}{1}

x=-2

Secondly consider,

\frac{y}{-9\times3-(-4)\times8}=\frac{1}{8\times2-3\times5}

\frac{y}{5}=\frac{1}{1}

y=5

Therefore, x = -2 and y = 5