Question

How do you solve this system of equations \[y=\dfrac{-3}{4}x\], \[x-4y=32\]?

Answer 1

Hint: This question belongs to the topic of algebra. For solving this question, we will first take the value of y from the equation \[y=\dfrac{-3}{4}x\] and put that value of the y in the equation \[x-4y=32\]. After doing some further process, we will find the value of x. And, after substituting or putting that value of x in any of the two given equations, then we will get the value of y.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to solve the system of equations using the equations \[y=\dfrac{-3}{4}x\] and \[x-4y=32\].
As we know that one equation is \[y=\dfrac{-3}{4}x\], so we will substitute this value of y in the equation \[x-4y=32\], we will get
\[x-4\left( \dfrac{-3}{4}x \right)=32\]
The above equation can also be written as
\[\Rightarrow x-\left( -3x \right)=32\]
We can write the above equation as
\[\Rightarrow x+3x=32\]
The above equation can also be written as
\[\Rightarrow 4x=32\]
Now, after dividing 4 to the both side of the above equation, we can write the above equation as
\[\Rightarrow x=\dfrac{32}{4}\]
As we know that when 32 is divided by 4, we will get 8. So, we can write the above equation as
\[\Rightarrow x=8\]
Now, we have got the value of x as 8.
Now, putting the value of x as 8 in the equation \[x-4y=32\], we will get
\[8-4y=32\]
We can write the above equation as
\[\Rightarrow -4y=32-8\]
The above equation can also be written as
\[\Rightarrow -4y=24\]
Now, diving -4 to the both side of the equation, we get
\[\Rightarrow \dfrac{-4y}{-4}=\dfrac{24}{-4}\]
The above equation can also be written as
\[\Rightarrow y=-6\]
Now, we have solved the system of equations \[y=\dfrac{-3}{4}x\] and \[x-4y=32\]
The solutions to the system of equations are x=8 and y=-6.

Note: As we can say that this question is from the topic of algebra, so we should have a better knowledge in that topic. Always remember that whenever we have asked to solve the system of two or three equations, then we will solve the equations and find the value of variables by substituting the value of variables in the equations.