solve for x and y
3x+2y=7;x+2y=9
Answers
Answer:
solve for x and y for the following Equations
\begin{gathered}\begin{array}{cccccc}3x&+&2y&=&7&---[1]\\x&+&2y&=&9&---[2]\\\end{array}\end{gathered}
3x
x
+
+
2y
2y
=
=
7
9
−−−[1]
−−−[2]
\begin{gathered}\\\end{gathered}
\underline{\underline{\Huge{\textbf{Solution:}}}}
Solution:
\underline{\huge{\textsf{Step-1:}}}
Step-1:
Consider Equation [2]
\begin{gathered}\begin{array}{ccccc}x&+&2y&=&9\\\end{array}\end{gathered}
x
+
2y
=
9
\begin{gathered}\\\end{gathered}
\underline{\huge{\textsf{Step-2:}}}
Step-2:
Multiply with 3 on both sides
\begin{gathered}\begin{array}{cccccc}3x&+&6y&=&27&---[3]\\\end{array}\end{gathered}
3x
+
6y
=
27
−−−[3]
\begin{gathered}\\\end{gathered}
\underline{\huge{\textsf{Step-3:}}}
Step-3:
Do [3]-[1] to get value of y
\begin{gathered}\begin{array}{cccccccc}&3x&+&&6y&=&&27\\&3x&+&&2y&=&&7\\-&&&-&&&-&\\&&&&4y&=&&20 \end{array}\end{gathered}
−
3x
3x
+
+
−
6y
2y
4y
=
=
=
−
27
7
20
\implies 4y = 20⟹4y=20
\implies y = 5⟹y=5
\begin{gathered}\\\end{gathered}
\underline{\huge{\textsf{Step-4:}}}
Step-4:
Substitute in [1] to get value of y
\begin{gathered}\begin{array}{ccccc}3x&+&2(5)&=&7\\\end{array}\end{gathered}
3x
+
2(5)
=
7
\implies 3x\: +\: 10\: =\: 7⟹3x+10=7
\implies 3x\: =\: 7\: -\: 10⟹3x=7−10
\implies 3x\: =\: -\:3⟹3x=−3
\implies x\: =\: -\:1⟹x=−1
\begin{gathered}\\\end{gathered}
\blacksquare\: \textsf{The Value of x and y satisfying given set of Equation are \underline{\textbf{-1\: and\: 5}}\: respectively}■The Value of x and y satisfying given set of Equation are
-1and5
respectively
Answer:
x=-1. and. y=5
Step-by-step explanation:
through elimination method