Question

Question 20>Solve the given linear system of equations:- 1212ySy8Enter your answer in the form of an ordered pair(x, y).One solution:O No solutionO Infinite number of solutions

Answer 1

the equation given was

`\begin{gathered} 9x-12y=-12 \\ -6x+8y=8 \end{gathered}`

now to solve this equation, we should solve the simultaneous equation and get the values of x and y

now, let's take equation 1 and solve for x

`\begin{gathered} 9x-12y=-12 \\ \text{make y the subject of formula} \\ 9x=-12+12y \\ \text{divide both sides by 9} \\ (9x)/(9)=(-12+12y)/(9) \\ x=(-12+12y)/(9) \end{gathered}`

put x into equation 2

`\begin{gathered} -6x+8y=8 \\ x=(-12+12y)/(9) \\ \text{put x into the equation} \\ -6((-12+12y)/(9))+8y=8 \\ (72-72y)/(9)+8y=8 \\ 8-8y+8y=8 \\ 0=0 \end{gathered}`

from the solution, y = 0

put y = 0 into either equation 1 or 2

from equation 1

`\begin{gathered} 9x-12y=-12 \\ \text{put y = 0} \\ 9x-12(0)=-12 \\ 9x-0=-12 \\ 9x=-12 \\ \text{divide both sides by 9} \\ (9x)/(9)=-(12)/(9) \\ x=-(4)/(3) \end{gathered}`

from the above calculation, the above equation has only one solution.

the ordered pair is

`(x,y)=(-(4)/(3),0)`