Question

Solve \[x-2y=7\] and \[x+y=-2\]?

Answer 1

Hint: We are given a question which has two equations in two variables and we are asked to solve it for the values of ‘x’ and ’y’. To solve the given pair of equations we will use the substitution method. From the first equation, we will write the expression in terms of ‘x’ which we will get it as, \[x=7+2y\] and then we will substitute it in the second equation to get the value of ‘y’. Then, we will substitute the value of ‘y’ in \[x=7+2y\] in order to get the value of ‘x’. Hence, we will have the values of ‘x’ and ‘y’.

Complete step by step solution:
According to the given question, we are a set of equations in two variables and we have to solve it for ‘x’ and ‘y’.
The equations that we have is,
\[x-2y=7\] and \[x+y=-2\]
Let us number the equations, that is,
\[x-2y=7\]-----(1)
\[x+y=-2\]-----(2)
In order to solve the given equations, we will use the substitution method.
So from the first equation, we will write the equation in terms of ‘x’, so we get,
\[x=7+2y\]----(3)
We will now substitute the equation (3) in equation (2) and so we get,
\[\left( 7+2y \right)+y=-2\]
We will now reduce the above expression further, we get,
\[\Rightarrow 7+2y+y=-2\]
\[\Rightarrow 7+3y=-2\]
We will now write the expression in terms of ‘y’ ad so we get,
\[\Rightarrow 3y=-2-7\]
\[\Rightarrow 3y=-9\]
So, we get the value of ‘y’ as,
\[\Rightarrow y=-3\]----(4)
Substituting equation (4) in equation (3), we get,
\[x=7+2\left( -3 \right)\]
Solving further, we get,
\[\Rightarrow x=7-6\]
\[\Rightarrow x=1\]

Therefore, we have the values of \[x=1\] and \[y=-3\].

Note: The solving of the given equations should be carried out in a clear and step wise. Also, the obtained values can be checked for its correctness. We just need to put the values of ‘x’ and ‘y’ in any one of the equations (1) or (2).
We are taking the equation (1) and we have the LHS as,
\[x-2y\]
Substituting the values of ‘x’ and ‘y’ in the above expression, we get,
\[\Rightarrow 1-2\left( -3 \right)\]
\[\Rightarrow 1+6\]
\[\Rightarrow 7=RHS\]
Therefore, the obtained answer is correct.