
How do you solve the system of equations \[2x+3y=13\] and \[x\,\,=\,2y\,-4\].
Answer
547.5k+ views
Hint: In the given question we have two equations. First we need to simplify it if the equation is jumbled. Then we have to determine the values of \[x\]and \[y\]. So we have to take equation \[2.\] and subtract it with equation \[1\]. Then we have to simplify it for getting the value of \['y'\] in the equation \[2\] for finding the remaining term. By using the above given condition, solve the given problem. Also we have to use the method of elimination for solving the given two equations by using multiplication and addition for eliminating the variable from the equation. After that we get the values from substitution.
Complete step by step solution:
Given that the equations:-
\[2x\,+3y=13\,\,\,\,..................\left( i \right)\]
\[x\,=\,2y\,-4\]
Multiply the above equation from \[2\] we get.
\[2x\,\,=\,4y\,-8\]
The equation is written as,
\[2x\,\,-\,4y\,\,=-8\,\,\,\,..............\left( 2 \right)\]
Now, we have to subtract the equation \[\left( 2 \right)\] from \[\left( 1 \right)\] we get,
\[2x\,\,+\,\,3y\,\,=13\]
\[-2x\,\,+\,4y\,\,=\,+8\]
Now have \[\,7y\,\,=21\]
So divide it by \[7\] we get
\[7y\,\,=\,21\]
\[y\,=\,3\]
After that we have to find the value of \[x\].
Put, the value of \[y\] in any equation \[50\] we take the equation \[\left( 2 \right)\],
\[x\,\,=2y-4\]
\[\therefore \,\,x\,=\,2\left( 3 \right)\,-4\]
\[\therefore \,\,x\,=\,\,6\,\,-4\]
\[\therefore \,\,x\,=\,\,2\]
Hence, we get the value of \[x\,=2\] and \[y\,=3\] by solving the given equation \[2x\,\,3y\,=\,13,\,\,\,\And \,\,x\,\,=\,2y\,\,-4\].
Note: When you are solving the problem check the given values. Then you get the idea that we have to find firstly you have to simplify the given equation by expanding. After that check the step whether you are solving the correct variable or not and substitute the proper value. Analyse the problem and totally check all the possibilities where you get wrong in the problem.
Complete step by step solution:
Given that the equations:-
\[2x\,+3y=13\,\,\,\,..................\left( i \right)\]
\[x\,=\,2y\,-4\]
Multiply the above equation from \[2\] we get.
\[2x\,\,=\,4y\,-8\]
The equation is written as,
\[2x\,\,-\,4y\,\,=-8\,\,\,\,..............\left( 2 \right)\]
Now, we have to subtract the equation \[\left( 2 \right)\] from \[\left( 1 \right)\] we get,
\[2x\,\,+\,\,3y\,\,=13\]
\[-2x\,\,+\,4y\,\,=\,+8\]
Now have \[\,7y\,\,=21\]
So divide it by \[7\] we get
\[7y\,\,=\,21\]
\[y\,=\,3\]
After that we have to find the value of \[x\].
Put, the value of \[y\] in any equation \[50\] we take the equation \[\left( 2 \right)\],
\[x\,\,=2y-4\]
\[\therefore \,\,x\,=\,2\left( 3 \right)\,-4\]
\[\therefore \,\,x\,=\,\,6\,\,-4\]
\[\therefore \,\,x\,=\,\,2\]
Hence, we get the value of \[x\,=2\] and \[y\,=3\] by solving the given equation \[2x\,\,3y\,=\,13,\,\,\,\And \,\,x\,\,=\,2y\,\,-4\].
Note: When you are solving the problem check the given values. Then you get the idea that we have to find firstly you have to simplify the given equation by expanding. After that check the step whether you are solving the correct variable or not and substitute the proper value. Analyse the problem and totally check all the possibilities where you get wrong in the problem.
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