Question

4x + 5y = 19 8x - 6y = -10

Answer 1

Given the system of equations :

`\begin{gathered} 4x+5y=19\rightarrow(1) \\ 8x-6y=-10\rightarrow(2) \end{gathered}`

Multiply the first equation by -2:

`\begin{gathered} -2\cdot4x+(-2)\cdot5y=-2\cdot19 \\ -8x-10y=-38\rightarrow(3) \end{gathered}`

Add the equations (2) and (3) to eliminate x :

`\begin{gathered} 8x-8x-6y-10y=-10-38 \\ -16y=-48 \\ \\ y=(-48)/(-16)=3 \end{gathered}`

Substitute with y in equation (1) to find x :

`\begin{gathered} 4x+5\cdot3=19 \\ 4x+15=19 \\ 4x=19-15 \\ 4x=4 \\ \\ x=(4)/(4)=1 \end{gathered}`

So, the solution of the system is :

`\begin{gathered} x=1 \\ y=3 \\ (x,y)=(1,3) \end{gathered}`