Question

Solve for x and y : $2x + y = 6$ and $2x - y = 2$.

Answer 1

Hint: - If a, b, and c are real numbers where a and b are not equal to 0 then $ax + b = c$ is called a linear equation in two variables where x and y are the two variables. The numbers a and b are called the coefficients of the equation $ax + b = c$. The number c is called the constant of the equation.

Complete step-by-step answer:
In this problem we have 2 linear equations with 2 unknowns
So, our first equation is:
 $2x + y = 6$
Re writing this equation we get:
$\Rightarrow y = - 2x + 6$ ------(i)
Our second equation is
$2x - y = 2$
Putting the value of $y = - 2x + 6$ from (i) in the above equation
$\Rightarrow 2x - ( - 2x + 6) = 2$
$\Rightarrow 2x + 2x - 6 = 2$
$\Rightarrow 4x = 2 + 6$
$\Rightarrow 4x = 8$
$\Rightarrow x = \dfrac{8}{4}$
$\Rightarrow x = 2$
Now putting the value of $x = 2$ in the equation $2x + y = 6$
$\Rightarrow 2(2) + y = 6$
$\Rightarrow 4 + y = 6$
$\Rightarrow y = 6 - 4$
$\Rightarrow y = 2$
Therefore, we get the value of $x = 2$ and $y = 2$

Note: - The method of solving "by substitution" works by solving one of the equations from one of the variables, and then putting the value obtained back into the other equation. Then we solve back the first variable. It is the simplest form of solving a linear equation with two variables. We can solve using the elimination method as well.