Question

How do you solve 3x+y=5 and x-2y=11 using substitution?

Answer 1

Hint: This question is from the topic of algebra. In this question, we will find out the value of x and y from the given equations. In solving this question, we will first find the value from the equation 3x+y=5. After that, we will put that value of y in the equation x-2y=11. After solving, we will get the value of x. After that, we will find the value of y by putting the value of x in any of those two equations.

Complete step by step solution:
Let us solve this question.
In this question, we have to find the value of x and y from the equations 3x+y=5 and x-2y=11 using the substitution method.
So, let us first take the equation 3x+y=5 and find the value of y in terms of x.
We can write the equation 3x+y=5 as
y=5-3x
Now, we will put this value of y in the second equation that is x-2y=11. We can write
\[x-2\left( 5-3x \right)=11\]
The above equation can also be written as
\[\Rightarrow x-2\times 5-2\left( -3x \right)=11\]
The above equation can also be written as
\[\Rightarrow x-10+6x=11\]
The above equation can also be written as
\[\Rightarrow x+6x=11+10\]
The above equation can also be written as
\[\Rightarrow 7x=21\]
Now, dividing 7 to both the side of equation, we can write
\[\Rightarrow \dfrac{7x}{7}=\dfrac{21}{7}\]
\[\Rightarrow x=3\]
Now, we will put this value of x as 3 in the equation 3x+y=5, we will get
\[3\times 3+y=5\]
The above equation can also be written as
\[\Rightarrow 9+y=5\]
The above equation can also be written as
\[\Rightarrow y=5-9=-4\]
Hence, we get the value of y as -4.
So, we have solved the equations 3x+y=5 and x-2y=11 using substitution and got the value of x as 3 and the value of y as -4.

Note: As we can see that this question is from the topic of algebra, so we should have a better knowledge in that topic. We can check if our answer is correct or not by putting the value of x and y as 3 and -4 respectively in both the equations. For solving the pair of linear equations we can use the elimination method where we eliminate any one of the variables and then put that value in another equation to find the remaining variable.