The system of equations we have is:
[tex]\begin{gathered} 4x+5y=22 \\ 4x+10y=8 \end{gathered}[/tex]Step 1. substract the second equation from the first equation to eliminate variable x:
[tex]\begin{gathered} 4x+5y=22 \\ -(4x+10y=8) \end{gathered}[/tex]The minus sign changes the signs of the second equation, and now we have:
[tex]\begin{gathered} 4x+5y=22 \\ -4x-10y=-8 \end{gathered}[/tex]and the result of this is:
Step 2. From the result of the substraction -5y=14, solve for y:
[tex]\begin{gathered} -5y=14 \\ y=\frac{14}{-5} \\ y=-2.8 \end{gathered}[/tex]Step 3. Substitute this value of y in the first original equation
[tex]4x+5y=22[/tex]To find the value of x.
We substitute y=-2.8
[tex]4x+5(-2.8)=22[/tex]Step 4. Solve for x
[tex]\begin{gathered} 4x-14=22 \\ 4x=22+14 \\ 4x=36 \\ x=\frac{36}{4} \\ x=9 \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=9 \\ y=-2.8 \end{gathered}[/tex]
