Question

How do you solve $3x+y=5$ and $2x-y=20$ using substitution?

Answer 1

Hint: We will use substitution method to solve the given equations as asked in the question. First, we will take the equation $2x-y=20$, and rewrite it in terms of $y$. We will then substitute the expression in terms of $y$ in the equation $3x+y=5$ and we will get the value of $x$. We will substitute this value of $x$ in the equation which we wrote in terms of $y$, and hence we get the value of $y$ as well.

Complete step by step answer:
According to the given question, we have been given a set of two equations with two variables each, so we have to solve for each of the two variables using a substitution method.
As the substitution name itself suggests that we will substitute the value of either $x$ or $y$ and solve for the other.
We will start as follows,
$3x+y=5$------(1)
$2x-y=20$------(2)
We will write the equation (2) in terms of $y$, we get,
$2x-y=20$
$\Rightarrow y=2x-20$----(3)
Substituting equation (3) in equation (1), we get,
$3x+y=5$
$\Rightarrow 3x+(2x-20)=5$
Solving the above expression further, we get,
$\Rightarrow 3x+2x-20=5$
Adding 20 in both sides of the equality, we get,
$\Rightarrow 3x+2x-20+20=5+20$
In the LHS, 20 will get cancelled and we will have separate x-terms and the constants. In the RHS, 20 gets added up to 5 and we get,
$\Rightarrow 3x+2x=5+20$
$\Rightarrow 5x=25$
$\Rightarrow x=5$
Now, we will substitute the value of $x=5$ in equation (5), we get,
$y=2x-20$
$\Rightarrow y=2(5)-20$
Solving the above expression, we have,
$\Rightarrow y=10-20$
$\Rightarrow y=-10$

Therefore, $x=5\And y=-10$.

Note: The values we obtain for $x$ and $y$ may or may not be correct. We can always check whether the answers are right or not by substituting in the equations given to us. We have,
$3x+y=5$
Taking LHS and substituting the values of $x$ and $y$, we get,
$3x+y$
$\Rightarrow 3(5)+(-10)$
$\Rightarrow 15-10$
$\Rightarrow 5=RHS$
Similarly, we can verify with the other equation as well. Therefore, we have the correct answer.