Question

How do you solve by substitution $0.3x - 0.2y = 0.5\;{\text{and}}\;x - 2y = - 5?$

Answer 1

Hint:In substitution method, we take the value of a variable from an equation in terms of other variable and then put the value of that variable in another equation and after solving that another equation, we will get the value of the other variable, so we put its value in any of the equations to get the value of the first variable.

Complete step by step solution:
In order to solve the given equations $0.3x - 0.2y = 0.5\;{\text{and}}\;x - 2y = - 5$ through substitution method, we will proceed as follows:
From one of the two equations, we will take value of one variable in terms of other,
$
\Rightarrow x - 2y = - 5 \\
\Rightarrow x = 2y - 5 - - - - - (i) \\
$
Now putting $x = 2y - 5$ in place of a in the second equation, we will get
$ \Rightarrow 0.3(2y - 5) + 0.2y = 0.5$
Opening the parentheses with help of commutative property of multiplication and solving this equation for value of b
$
\Rightarrow 0.3 \times 2y - 0.3 \times 5 + 0.2y = 0.5 \\
\Rightarrow 0.6y - 1.5 + 0.2y = 0.5 \\
$
Adding one and half to both sides of the equation, we will get
$
\Rightarrow 0.6y + 0.2y = 0.5 + 1.5 \\
\Rightarrow 0.8y = 2.0 \\
$
Now, dividing both sides of the equation with coefficient of y, we will get
$
\Rightarrow \dfrac{{0.8y}}{{0.8}} = \dfrac{{2.0}}{{0.8}} \\
\Rightarrow y = 2.5 \\
$
So we got the value of $y = 2.5$
Now putting the value of y in equation (i), to get the value of the other variable, that is x
$
\Rightarrow x = 2 \times 2.5 - 5 \\
\Rightarrow x = 5 - 5 \\
\Rightarrow x = 0 \\
$
Therefore $x = 0\;{\text{and}}\;y = 2.5$ is the required solution of the given equations.

Note: We have selected the second equation to get the variable value in expression form because you can see that the first equation is a bit complex than the second one, as it has the coefficients of its variable in decimals. So if we have gone with the first one then the variable value in expressional form has been complex.