Question

Solve equations using substitution method:
$5x-2y=10$ and $4x-6y=3$

• A. $\frac{-27}{11}$ and $\frac{25}{22}$
• B. $\frac{27}{11}$ and $\frac{-25}{22}$
• C. $\frac{27}{11}$ and $\frac{25}{22}$
• D. $\frac{-27}{11}$ and $\frac{-25}{22}$

Answer 1

The correct option is C $\frac{27}{11}$ and $\frac{25}{22}$

$5x-2y=10$ ------- (1)
$4x-6y=3$------ (2)
From equation 1:-
$2y=10-5x$
$2y=-10+5x$
$Y=\frac{-10+5x}{2}$
Substitute the value of y in equation 2:
$4x-6y=3$
$4x6\left(\frac{-10+5x}{2}\right)=3$
$4x3(-10+5x)=3$
$4x+3015x=3$
$-11x=3-30$
$-11x=-27$
$X=\frac{27}{11}$
Now, Substitute $x=\frac{27}{11}$ in equation 1:
$5\left(\frac{27}{11}\right)-2y=10$
$\frac{135}{11}2y=10$
$13522y=10x11$
$135110=22y$
$25=22y$
$Y=\frac{25}{22}$
Therefore the solution is:$X=\frac{27}{11}$ and $Y=\frac{25}{22}$