Question

Solve the simultaneous equations using an algebraic method:

2x+5y=0
3x-4y=23

Answer 1

Answer: The required solution is (x, y) = (5, -2).

Step-by-step explanation: We are given to solve the following system of equations :

`2x+5y=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\3x-4y=23~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)`

From equation (i), we have

`2x+5y=0\\\\\Rightarrow 2x=-5y\\\\\Rightarrow x=-(5)/(2)y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)`

Substituting the value of x from equation (iii) in equation (ii), we get

`3*\left(-(5)/(2)y\right)-4y=23\\\\\\\Rightarrow -15y-8y=46\\\\\Rightarrow -23y=46\\\\\Rightarrow y=-(46)/(23)\\\\\Rightarrow y=-2.`

From equation (iii), we get

`x=-(5)/(2)*(-2)=5.`

Thus, the required solution is (x, y) = (5, -2).