Question

Solve the given linear equation: 2x-7y=7; 3x+y=22.

Answer 1

- Hint: In the above equation the given equations are linear equations in 2 variables x and y and we need to find the possible values of x and y such that both the equations are satisfied. We can use the method of elimination to solve the pair of equations given in the question.

Complete step-by-step solution -

Before starting with the solution, let us discuss the significance of linear equations in two variables. Linear equations in two variables represent the equation of a line on the Cartesian plane.
Now to start with the question, let us note down the equations given in the question.
2x-7y=7…………..(i)
3x+y=22………….(ii)
Now we will try to eliminate y from by adding equation (i) with 7 times of the equation (ii). On doing so, we get
2x-7y+21x+7y=7+154
\[\Rightarrow 23x=161\]
\[\Rightarrow x=\dfrac{161}{23}\]
\[\Rightarrow x=7\]
Now we will put the value of x in equation (ii).
3x+y=22
\[\Rightarrow 3\times 7+y=22\]
\[\Rightarrow y=1\]
Therefore, the value of (x,y) is equal to (7,1).

Note: Be careful with the signs and calculations as in such questions, the possibility of making a mistake is either of the sign or a calculation error. Also, we should be clear that a solution can represent different geometries when represented in planes with different dimensions, and all the points lying on these geometries would represent a solution to the linear equation. For example: when the solution of the above equation is represented on a number line, i.e., a single dimensioned plane, the geometry formed is just a point while on the Cartesian plane, it is represented by a straight line. Further, if we extend it to a 3-D plane, we will find the same solution will represent a plane.