Question

How do you solve this system of equations: \[-8x-y=14\] and \[-5x+y=12\]?

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 one variable from any one equation and put that value in the second equation. From there, we will find the value of any one variable. After that, using any of the two equations, we will find the value of the other variable.

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 \[-8x-y=14\] and \[-5x+y=12\]. That means we have to find the value of x and y from these equations.
We will use a substitution method to solve this question.
The equation \[-5x+y=12\] can also be written as
\[y=5x+12\]
Now, we get the value of y as 5x+12 from the equation \[-5x+y=12\].
Now, putting this value of y in the equation \[-8x-y=14\], we get
\[-8x-\left( 5x+12 \right)=14\]
The above equation can also be written as
\[\Rightarrow -8x-5x-12=14\]
The above equation can also be written as
\[\Rightarrow -8x-5x=14+12\]
The above equation can also be written as
\[\Rightarrow -13x=26\]
The above equation can also be written as
\[\Rightarrow x=-2\]
Hence, we get that the value of x is -2.
Now, putting the value of x as -2 in the equation \[-5x+y=12\], we get
\[-5\left( -2 \right)+y=12\]
The equation can also be written as
\[\Rightarrow 10+y=12\]
The above equation can also be written as
\[\Rightarrow y=12-10=2\]
Hence, we get that the value of y is 2.
So, we can say that the solutions to the system of equations are x=-2 and y=2.

Note: We should have a better knowledge in the topic of algebra to solve this type of question easily. We can solve this question by another method.
The other method is elimination method. We will eliminate the term y from the equations \[-8x-y=14\] and \[-5x+y=12\].
We will add those two equations.
\[\left( -5x+y \right)+\left( -8x-y \right)=12+14\]
The above equation can also be written as
\[\Rightarrow -5x+y-8x-y=12+14\]
The above equation can also be written as
\[\Rightarrow -13x+0=26\]
\[\Rightarrow x=\dfrac{26}{-13}\]
From the above equation, we can say that the value of x is -2. Now, we can find the value of y from the equation \[-5x+y=12\] by putting the value of x as -2.
We can write the equation \[-5x+y=12\] as
\[-5\left( -2 \right)+y=12\]
The equation can also be written as
\[\Rightarrow 10+y=12\]
From the above equation, we can say that the value of y is 2.