Question

How do you solve the pair of linear equations \[5x+4y=-1\] and \[2x+y=-4\]?

Answer 1

Hint: In this problem, we have to solve and find the value of x and y. We can solve these given equations using elimination methods. We can multiply the number 4 in the second equation. We can then subtract the new equation and the first equation, we will eliminate one variable and we can find the value for one of the variables, we can then substitute the value in one of the equations to get the value of another variable.

Complete step by step solution:
We know that the given equations to be solved are,
\[\Rightarrow 5x+4y=-1\]…….. (1)
\[\Rightarrow 2x+y=-4\]……… (2)
We can now multiply the number 4 to the equation (2), we get
\[\Rightarrow 8x+4y=-16\]…… (3)
We can now subtract the equation (1) and the equation (3), we get
\[\Rightarrow 5x+4y+1-8x-4y-16=0\]
We can now simplify the above step, we get
\[\Rightarrow -3x-15=0\]
We can now add 15 on both sides, we get
\[\Rightarrow -3x=15\]
We can divide the number -3 on both sides, we get
\[\Rightarrow x=-5\]
We can now substitute the value of x in equation (2), we get
\[\begin{align}
  & \Rightarrow 2\left( -5 \right)+y=-4 \\
 & \Rightarrow y=6 \\
\end{align}\]
Therefore, the value of x = -5 and y = 6.

Note: Students make mistakes while multiplying numbers in order to eliminate any one of the variables to get the value of another while subtracting. We can substitute the resulting values to check for the correct answer.
We can substitute x = -5 and y = 6 in equation (2), we get
\[\Rightarrow 2\left( -5 \right)+6=-4\]
Therefore, the values are correct.