Question

Solve the simultaneous equations using an algebraic method: 2x+5y=0 3x-4y=23

Answer 1

i searched up a different question and it put this one iive done this so many times

Answer 2

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

$2x+5y=0\\\\\Rightarrow 2x=-5y\\\\\Rightarrow x=-\dfrac{5}{2}y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

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

$3\times\left(-\dfrac{5}{2}y\right)-4y=23\\\\\\\Rightarrow -15y-8y=46\\\\\Rightarrow -23y=46\\\\\Rightarrow y=-\dfrac{46}{23}\\\\\Rightarrow y=-2.$

From equation (iii), we get

$x=-\dfrac{5}{2}\times(-2)=5.$

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