Question

How do I find two solutions for both x and y with only two equations provided ?

Answer 1

Hint: In the given question, we need to tell how we can find two solutions for both x and y when we are provided two simultaneous equations in two variables, x and y. There are various methods to solve two given equations in two variables like substitution method, cross multiplication method, elimination method, matrix method and many more. The equations given in the question can be solved using any one of the above mentioned methods easily.

Complete step by step solution:
So, we are provided with two linear equations in two variables x and y.
A system of two simultaneous linear equations in variables x and y can have a unique solution, infinitely many solutions or no solution at all depending upon the conditions.
A system of two simultaneous linear equations may have infinitely many solutions if both the equations represent the exact same line on the coordinate plane.
A system of two simultaneous linear equations may have a unique solution if both the equations represent lines intersecting a single point.
A system of two simultaneous linear equations may have no solution at all if both the equations represent parallel lines on the coordinate plane.
So, there can either be a unique solution, no solution at all or infinite solutions for a system of linear equations in two variables. Hence, there can’t be just two solutions for both x and y.

Note: Linear Equation in two variables: A equation consisting of 2 variables having degree one is known as Linear Equation in two variables. Standard form of Linear Equation in two variables is $ax + by + c = 0$ where a, b and c are the real numbers and a, b which are coefficients of x and y respectively are not equal to 0. In the substitution method, we substitute the value of one variable from an equation into another equation so as to get an equation in only one variable.