Question

Solve equations using substitution method:
$2x+y=5$ and $2x-3y=3$

• A. $\frac{1}{4}$ and $\frac{-1}{2}$
• B. $\frac{1}{4}$ and $\frac{1}{2}$
• C. $\frac{-9}{4}$ and $\frac{-1}{2}$
• D. $\frac{9}{4}$ and $\frac{1}{2}$

Answer 1

Answer: (D)

$\frac{9}{4}$ and $\frac{1}{2}$

$2x+y=5$ ------- (1)
$2x-3y=3$------ (2)
From equation 1 :
$y=5-2x$
Substitute the value of y in equation 2 :
$2x-3(5-2x)=3$
$2x-15+6x=3$
$8x=3+15$
$x=\frac{18}{8}=\frac{9}{4}$
Now, Substitute $x=\frac{9}{4}$ in equation 1 :
$2\left(\frac{9}{4}\right)+y=5$
$18+4y=20$
$4y=20-18$
$y=\frac{2}{4}$
$y=\frac{1}{2}$
Therefore the solution is: $x=\frac{9}{4}$ and $y=\frac{1}{2}$