Question

Solve by substitution:

$x+y=2and3x+2y=5$

Answer 1

Step 1: Write $x$ in terms of $y$ from first equation

$\begin{array}{rcl}x+y& =& 2.....................\left(i\right)\\ 3x+2y& =& 5....................\left(ii\right)\end{array}$

From equation (i) we get $x=2-y.......\left(iii\right)$

Step 2: Substitute the value of $x$ in second equation

Putting this value of $x$ into (ii), we get

$\begin{array}{rcl}3\left(2-y\right)+2y& =& 5\\ & \Rightarrow & 6-3y+2y=5\\ & \Rightarrow & 6-y=5\\ & \Rightarrow & y=6-5\\ & \Rightarrow & y=1\end{array}$

Step 3: Substitute the value of $y$ in third equation we obtained

Putting this value of $y$, in $x=2-y$, we get

$\begin{array}{rcl}x& =& 2-y\\ & \Rightarrow & x=2-1\\ & \Rightarrow & x=1\end{array}$

Hence, the solution of the equation is $x=1,y=1$