3x-7y=7 11x+5y=87 and 5x+4y =43. Can the Following Equations Hold Simultaneously ? [ICSE Class 9 ML Aggarwal Solution Chapter-5 Exercise 5.2 Simultaneous Linear Equations Solution]
Given Equations are
3x-7y=7 —-(i)
11x+5y=87 —(ii)
and 5x+4y =43 —-(iii)
Multiplying Equation (i) by 5 and Equation (ii) by 7 we get,
15x -35y=35 —(iv)
77x+35y= 609 —(v)
Now Adding Equations (iv) and (v) we get,
15x -35y + 77x+35y = 35+609
⟹ 92x = 644
⟹ x = $\frac{644}{92}$
⟹ x = 7
Substituting the Value of x in Equation (i) we get,
3(7) -7y = 7
⟹ 21 -7y =7
⟹ 7y = 21 -7
⟹ 7y = 14
⟹ y = $\frac{14}{7}$
⟹ y =2
Now Substituting the Values of x and y in Equation (iii) we get,
5(7)+4(2) =43
⟹ 35 + 8 =43
⟹ 43 = 43
Clearly the Values of x and y Satisfy the Equation (iii) . therefore the Equations Holds Simultaneously.