Question

How do you solve the system of equations \[2x + y - 4 = 0\] and \[2x - y = 4\] ?

Answer 1

Hint: In this question, we have to solve the given algebraic equations.
First, we need to express one variable of the first equation in terms of the other variable. Then, put this in the second equation we will get the value of one variable. After putting the value of that variable in the first equation, we will get the value of the other variable and the required solution.

Complete step-by-step solution:
It is given that, \[2x + y - 4 = 0\] and \[2x - y = 4\] .
We need to solve the two equations.
Now, \[2x + y - 4 = 0\] ….....…. (i)
\[2x - y = 4\] ………….. (ii)
From equation (i) we get,
\[2x + y - 4 = 0\]
Or, \[y = 4 - 2x\] ……….... (iii)
Putting the value of y from (iii), in (ii) we get,
\[2x - y = 4\]
Or, \[2x - \left( {4 - 2x} \right) = 4\]
Simplifying we get,
\[2x - 4 + 2x = 4\]
Or, \[4x = 4 + 4 = 8\]
Or, \[x = \dfrac{8}{4} = 2\]
Putting the value of x in equation (i) we get,
\[2x + y - 4 = 0\]
\[y = 4 - 2 \times 2\]
Simplifying we get, \[y = 4 - 4 = 0\]
Therefore, we get,
\[x = 2,y = 0\]

Hence the solution of the system of equations \[2x + y - 4 = 0\] and \[2x - y = 4\] is \[x = 2,y = 0\].

Note: Two equations with the same variables are called systems of equations and the equations in the system are called simultaneous equations. To solve a system of equations means to find an ordered pair of numbers that satisfies both the equations in the system.
We can solve the system of linear equations by the following methods:
Elimination method
Substitution method
Elimination method:
In the elimination method, the object is to make the coefficient of one variable the same in both equations so that one variable can be eliminated either by adding the equations together or by subtracting one from the other.
Substitution method:
In the substitution method, one equation is manipulated to express one variable in terms of the other. Then the expression is substituted in the other equation.