Question

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

Answer 1

Hint: To solve this question we will be using substitution method. We will take the first equation $3x+y=3$, and write this equation in terms of $y$. We will substitute this expression in terms of $y$ in the equation $2x+3y=-5$ and find the value of $x$. The value of $x$ is then substituted in the equation which we wrote in terms of $y$ and solve it to get the value of $y$.

Complete step by step answer:
According to the question given, we have to solve for $x$ and $y$, for the given set of equations using the substitution method.
In this method, we will express one equation in terms of one of the variables and substitute in the other equation and find the value of both the variables consecutively.
We have,
$3x+y=3$----(1)
 $2x+3y=-5$-----(2)
We will now express the equation (1) in terms of $y$, we have,
$3x+y=3$
$\Rightarrow y=3-3x$-----(3)
Substituting the equation (3) in the equation (2), we get,
$2x+3y=-5$
$\Rightarrow 2x+3(3-3x)=-5$
Opening up the brackets and multiplying the terms we have,
$\Rightarrow 2x+3(3)-3(3x)=-5$
On solving, we get,
$\Rightarrow 2x+9-9x=-5$
Now, we have to separate the x-terms and the constants, we have,
$\Rightarrow 2x+9-9x-9=-5-9$
Here, we have subtracted 9 from both sides of the equality and the equality stays intact. We will now solve the above expression, we get,
$\Rightarrow 2x-9x=-5-9$
\[\Rightarrow -7x=-14\]
\[\Rightarrow x=2\]
Now, putting the value of \[x=2\] in the equation (3),we get,
\[y=3-3x\]
\[\Rightarrow y=3-3(2)\]
\[\Rightarrow y=3-6\]
\[\Rightarrow y=-3\]

Therefore, \[x=2,y=-3\].

Note: The above solution used substitution method, we can also use elimination method, etc. to solve the above equations. In the substitution method, care should be taken while expressing the equation in terms of one variable as it is the critical part of this method. Further, the calculation of the values for each of the variables should be done correctly as well.