Question

Which of the following is the solution for the given system of two linear equations $x+y=2$ and $2x-y=3?$

• A. $(\frac{5}{3},\frac{1}{3})$
• B. $(\frac{1}{3},\frac{5}{3})$
• C. $(\frac{5}{3},\frac{-1}{3})$
• D. $(\frac{-5}{3},\frac{1}{3})$

Answer 1

The correct option is A $(\frac{5}{3},\frac{1}{3})$

Given lines are:
$x+y=2\dots \left(1\right)$
$2x-y=3\dots \left(2\right)$
Step 1: Multiplying by $2$ in equation$\left(1\right)$, we get
$2\times (x+y)=2\times 2$
$2x+2y=4\dots \left(3\right)$
Step 2: Substracting equation$\left(2\right)$ from equation$\left(3\right)$
$(2x+2y)-(2x-y)=4-3$
$3y=1$
$y=\frac{1}{3}$
Step 3: Plugging $y=\frac{1}{3}$ into equation$\left(1\right)$, we get
$x+\frac{1}{3}=2$
$x=2-\frac{1}{3}$
$x=\frac{5}{3}$

Answer:
$(x,y)=(\frac{5}{3},\frac{1}{3})$