Question

How do you solve \[35x-5y=20\] and \[y=7x+4\] using substitution?

Answer 1

Hint: This question belongs to the topic of algebra. We will solve the equations using the substitution method. In this question, we will first find out the value of one variable from the equation \[35x-5y=20\]. After that, we will put the value of that variable in equation \[y=7x+4\]. After solving, we will get the value of one variable. From there, we will find out the value of other variables.

Complete step by step answer:
Let us solve this question.
In this question, we have to solve \[35x-5y=20\] and \[y=7x+4\] using substitution. That means we have to find the value of x and y from these equations using a substitution method.
We can write the equation \[35x-5y=20\]as
\[-5y=20-35x\]
In the above equation, multiplying -1 to the both side of equation, we get
\[\Rightarrow 5y=-20+35x\]
After dividing 5 to both side of equation, we will get
\[\Rightarrow y=-4+7x\]
From here, we get that the value of y is \[-4+7x\]
Now, putting this value of in the equation \[y=7x+4\], we get
\[-4+7x=7x+4\]
We can write the above equation as
\[\Rightarrow 7x-7x=4+4\]
The above equation can also be written as
\[\Rightarrow 0=8\]
The above equation can never be correct.
Hence, we do not have any value of x from here.
So, we can say that the equations \[35x-5y=20\] and \[y=7x+4\] will not have any solutions of x and y.

Note:
We should have a better knowledge in the topic of algebra for solving this type of question easily. Always remember that in substitution method, we first find out the value of any one variable by solving any one of the equations. After that, we will put or substitute that value of variable to another equation to get the value of another variable. By putting or substituting the value of the second variable in any one of the equations, we will find the value of the first variable.