Question

If \[\left( x+3,4-y \right)=\left( 1,7 \right)\] then \[\left( x-3,4+y \right)\] is equal to
(a) \[\left( -2,-3 \right)\]
(b) \[\left( -5,1 \right)\]
(c) \[\left( 3,4 \right)\]
(d) None of these

Answer 1

Hint: Given that, \[\left( x+y,4-y \right)=\left( 1,7 \right)\]. Equate them and get the value of x and y. Then substitute the value of x and y in \[\left( x-3,4+y \right)\] to get its values.

Complete step-by-step answer:
The solution of an equation is the set of all values that, when substituted for unknowns, makes an equation true. For an equation having one unknown, we can use two fundamental rules of algebra i.e, additive property and multiplicative property. We can determine the solution for the same.
Now, we have given \[\left( x+3,4-y \right)=\left( 1,7 \right)\], which means that the coordinates \[\left( x-3,4+y \right)\] is equal to the coordinates \[\left( 1,7 \right)\]. We need to find the value of x and y from it.
\[\left( x+3,4-y \right)=\left( 1,7 \right)\]
Thus we can write it as, \[x+3=1\] and \[4-y=7\].
Thus let us solve and find the value of x and y.
\[x+3=1\Rightarrow x=1-3=-2\]
i.e. \[x=-2\]
\[4-y=7\Rightarrow y=4-7=-3\]
i.e. \[y=-3\]
Thus we got the value of \[x=-2\] and \[y=-3\].
Now we need to find the value of \[\left( x-3,4+y \right)\]. Substitute the value of x and y to it.
\[\therefore \left( x-3,4+y \right)=\left( -2-3,4-3 \right)=\left( -5,1 \right)\]
Hence, we got \[\left( x-3,4+y \right)=\left( -5,1 \right)\].
\[\therefore \] Option (b) is the correct answer.

Note: The value of \[x=-2\] and \[y=-3\], make us the solution set of the equation. We have used the fundamental rule of algebra. i.e. additive property.