To solve this question, let's choose the substitution method. So, you can follow the steps to find x and y.
Step 1: Isolate x in the first equation.
To isolate x:
First, subtract 6y from each side of the equation.
Second, divide both sides by 3.
[tex]\begin{gathered} 3x+6y=0 \\ 3x+6y-6y=0-6y \\ 3x=-6y \\ \frac{3x}{3}=\frac{-6y}{3} \\ x=-2y \end{gathered}[/tex]Step 2: Substitute x by -2y in the second equation.
[tex]\begin{gathered} 4x=2y-10 \\ 4\cdot(-2y)=2y-10 \\ -8y=2y-10 \end{gathered}[/tex]Step 3: Isolate y in the equation found in step 2.
To isolate y:
First, subtract 2y from both sides of the equation.
Second, divide both sides by -10.
[tex]\begin{gathered} -8y=2y-10 \\ -8y-2y=2y-10-2y \\ -10y=-10 \\ \frac{-10y}{-10}=\frac{-10}{-10} \\ y=1 \end{gathered}[/tex]Step 4: Find x by using the relation found in step 1.
Use the equation found in step 1 and substitute y by 1.
[tex]\begin{gathered} x=-2y \\ x=-2\cdot(1) \\ x=-2 \end{gathered}[/tex]Answer:
x = -2 and y = 1
or
(-2, 1)
