Q4 of 92 Page 73

Let us solve the following simultaneous equations in two variables by the method of substitution and check whether the solutions satisfy the equations.


Given … (1)


And … (2)


Expressing x of equation (1) in terms of y,



⇒ x + y = 3xy


∴ x = 3xy – y … (3)


Substituting (3) in (2),





⇒ 3xy – 2y = xy


⇒ 3xy – xy = 2y


⇒ 2xy = 2y


∴ x = 1


Substituting x value in (3),


⇒ x = 3xy – y


⇒ 1 = 3(1) y – y


⇒ 1 = 3y – y


⇒ 1 = 2y


∴ y = 1/2


∴ By solving, x = 1 and y = 1/2.


Justification:


(1) -




⇒ 3 = 3


And (2) -




⇒ 1 = 1


∴ We can see that x = 1 and y = 1/2 satisfy equations (1) and (2).


More from this chapter

All 92 →
4

Let us solve the following simultaneous equations in two variables by the method of substitution and check whether the solutions satisfy the equations.


 4

Let us solve the following simultaneous equations in two variables by the method of substitution and check whether the solutions satisfy the equations.


 4

Let us solve the following simultaneous equations in two variables by the method of substitution and check whether the solutions satisfy the equations.


 5

Let us solve the following simultaneous equations in two variables by the method of substitution.

2(x – y) = 3


5x + 8y = 14