Question

I need this math question it be solved thank you :)

Answer 1

The given system of equations is:

`\begin{gathered} 5x-4y=-10\text{ Eq.(1)} \\ 3x+2y=16\text{ Eq.(2)} \end{gathered}`

Start by solving for x in equation 1:

`\begin{gathered} 5x-4y=-10 \\ 5x=-10+4y \\ x=(-10+4y)/(5) \\ x=-(10)/(5)+(4y)/(5) \\ x=-2+(4y)/(5)\text{ Eq.(3)} \end{gathered}`

Now, replace this into equation 2:

`\begin{gathered} 3(-2+(4y)/(5))+2y=16 \\ \text{Apply the distributive property} \\ 3\cdot(-2)+3\cdot(4y)/(5)+2y=16 \\ -6+(12y)/(5)+2y=16 \\ (12y)/(5)+2y=16+6 \\ (12y)/(5)+2y=22 \\ (12y+5\cdot2y)/(5)=22 \\ (12y+10y)/(5)=22 \\ (22y)/(5)=22 \\ 22y=22\cdot5 \\ y=(22\cdot5)/(22) \\ \text{Simplify} \\ y=5 \end{gathered}`

Now, replace the y-value into Eq.(3) and find x:

`\begin{gathered} x=-2+(4\cdot5)/(5) \\ \text{Simplify} \\ x=-2+4 \\ x=2 \end{gathered}`

Now, let's check these values into the system of equations:

`\begin{gathered} 5\cdot2-4\cdot5=-10\text{ Eq.(1)} \\ 10-20=-10 \\ -10=-10\text{ O.K.} \\ 3\cdot2+2\cdot5=16\text{ Eq.(2)} \\ 6+10=16 \\ 16=16\text{ O.K.} \end{gathered}`

Answer: x=2 and y=5