Question

solve the pair of linear equations 3 x + 2 y =22 and 5 x - 3 y = 5 by the method of substitution​

Answer 1

Step-by-step explanation:

Let

\begin{gathered}3x+2y=22....eqn1 \\5x-3y=5....eqn2\end{gathered}

3x+2y=22....eqn1

5x−3y=5....eqn2

⇒

to use the method of substitution, we solve for one of the variables first

choosing eqn 2

\begin{gathered}5x-3y=5\\5x=5+3y\\x=\frac{5+3y}{5}\end{gathered}

5x−3y=5

5x=5+3y

x=

5

5+3y

⇒

substituting x=\frac{5+3y}{5}x=

5

5+3y

in eqn 1 ⇒

\begin{gathered}3(\frac{5+3y}{5} )+2y=22\\(\frac{15+9y}{5} )+2y=22\\\frac{15+9y+10y}{5} =22\\15+19y=110\\19y=110-15\\19y=95\\y=5\end{gathered}

3(

5

5+3y

)+2y=22

(

5

15+9y

)+2y=22

5

15+9y+10y

=22

15+19y=110

19y=110−15

19y=95

y=5

⇒

substituting y=5 in eqn ...2

\begin{gathered}5x-3(5)=5\\5x-15=5\\5x=5+15\\5x=20\\x=4\end{gathered}

5x−3(5)=5

5x−15=5

5x=5+15

5x=20

x=4

hope it is helpful for you