Given:
The equations are
[tex]2x+5y=0[/tex]
[tex]3x-4y=23[/tex]
To find:
The solution of given system of equations.
Solution:
We have,
[tex]2x+5y=0[/tex] ...(i)
[tex]3x-4y=23[/tex] ...(ii)
From (i), we get
[tex]2x=-5y[/tex]
[tex]x=-\dfrac{5y}{2}[/tex] ...(iii)
Putting this value in (ii), we get
[tex]3(-\dfrac{5y}{2})-4y=23[/tex]
[tex]-\dfrac{15y}{2}-4y=23[/tex]
[tex]\dfrac{-15y-8y}{2}=23[/tex]
[tex]-23y=2\times 23[/tex]
[tex]y=\dfrac{46}{-23}[/tex]
[tex]y=-2[/tex]
Putting y=-2 in (iii), we get
[tex]x=-\dfrac{5(-2)}{2}[/tex]
[tex]x=-\dfrac{-10}{2}[/tex]
[tex]x=\dfrac{10}{2}[/tex]
[tex]x=5[/tex]
Therefore, the solution of given system of equation is (5,-2).
