Question

How do you solve this system of equations: \[8x+5y=38\] and \[-8x+2y=4\]?

Answer 1

Hint: This question belongs to the topic of algebra. For solving this question, we will use a substitution method. Using the substitution method, we will take the value of \[8x\] from the equation \[8x+5y=38\] and put that value of \[8x\] in the equation \[-8x+2y=4\]. From there, we will find the value of the variable y. After that, using any of the two equations, we will find the value of the variable x.

Complete step by step solution:
Let us solve this question.
In this question, we have asked to solve the system of two equations. The equations are \[8x+5y=38\] and \[-8x+2y=4\]. We will use these two equations and find the value of x and y.
We will use a substitution method to solve this question.
The equation \[8x+5y=38\] can also be written as
\[8x=38-5y\]
Now, we will put this value of \[8x\] in the equation \[-8x+2y=4\] to get the value of y.
So, after putting the value of \[8x\], we can write
\[-\left( 38-5y \right)+2y=4\]
We can write the above equation as
\[\Rightarrow -38+5y+2y=4\]
We can write the above equation as
\[\Rightarrow -38+7y=4\]
The above equation can also be written as
\[\Rightarrow 7y=4+38=42\]
The above equation can also be written as
\[\Rightarrow y=\dfrac{42}{7}=6\]
Hence, we get that the value of y is 6. Now, putting the value of y as 6 in the equation \[8x+5y=38\], we get
\[8x+5\left( 6 \right)=38\]
The above equation can also be written as
\[\Rightarrow 8x+30=38\]
The above equation can also be written as
\[\Rightarrow 8x=38-30=8\]
The above equation can also be written as
\[\Rightarrow x=\dfrac{8}{8}=1\]
Hence, we get that the value of x is 1.
So, the solutions to given equations in the question are y=6 and x=1.

Note: We can solve this question by alternate method.
The second method for solving is elimination method. For that method, we will add both the equations. We will get
\[\left( -8x+2y \right)+\left( 8x+5y \right)=4+38\]
The above equation can also be written as
\[\Rightarrow 2y+5y=42\]
The above equation can also be written as
\[\Rightarrow y=\dfrac{42}{7}=6\]
Now, we will put the value of y as 6 in the equation \[8x+5y=38\], we will get
\[8x+5\left( 6 \right)=38\]
The above equation can also be written as
\[\Rightarrow x=\dfrac{38-30}{8}=1\]
Hence, we get the value of x is 1 and the value of y is 6.