Question

How do you solve the following system:
 $ - 3x + 8y = - 7,2x + 2y = 4 $ ?

Answer 1

Hint: The above given systems of equations are the systems of linear equations with two variables $ x $ and \[y\]. The following system of equations can easily be solved by the method of substitution that we have studied in earlier classes. The second equation here can easily be divided by $ 2 $ which will then render the second equation as:
 $ x + y = 2 $
The value of one variable (either one of them)from any of the equations can then be substituted into the other equation and then the equation will then become equation in one variable which can then be easily solved and then substitute value which is obtained into the other equation.

Complete step by step solution:
We are given the equations we will first solve the first equation and then proceed to solve the next equation. Value from one equation will be put into the other equation.
The given equations are
 $ - 3x + 8y = - 7,2x + 2y = 4 $
The second equation can be rewritten as:
 $ x + y = 2 $
The value of $ x $ from the first equation can be written as:
 $ x = \dfrac{{(8y + 7)}}{3} $
This value will now be elegantly substituted into the second equation which will yield us with:
 $ \dfrac{{(8y + 7)}}{3} + y = 2 $
 $ 8y + 7 + 3y = 6 $ $ $
 $ 11y = - 1 $
Upon further solving the above given equation we get the value of the variable $ y $ as
 $ y = - \dfrac{1}{{11}} $
And then substituting the given value of $ y $ into first equation we get
 $ - 3x - 8*(\dfrac{1}{{11}}) = - 7 $
We get $ x = \dfrac{{23}}{{11}} $
Thus we have solved the given system of equation for both the variables and we get our answer as:
 $ x = \dfrac{{23}}{{11}} $ and $ y = - \dfrac{1}{{11}} $
So, the correct answer is “ $ x = \dfrac{{23}}{{11}} $ and $ y = - \dfrac{1}{{11}} $ ”.

Note: The above equation can also be solved by adjusting one equation to the second equation by multiplying the first equation by a number that will render calculation easy going forward but the above method of substitution works best for such a type of question and should be applied.