Sure, let's solve the equation step-by-step:
The given equation is:
[tex]\[2x + y = 0\][/tex]
Step 1: Isolate y in terms of x.
First, we can rearrange this equation to solve for [tex]\(y\)[/tex]:
[tex]\[y = -2x\][/tex]
Step 2: Choose a specific value for [tex]\(x\)[/tex].
Since there are infinitely many solutions to this equation (as it is a linear equation with two variables), we can choose a specific value for [tex]\(x\)[/tex] to find a particular solution.
Let's assume [tex]\(x = 1\)[/tex].
Step 3: Substitute the chosen value of [tex]\(x\)[/tex] back into the equation for [tex]\(y\)[/tex].
Substitute [tex]\(x = 1\)[/tex] into the equation [tex]\(y = -2x\)[/tex]:
[tex]\[y = -2(1)\][/tex]
Step 4: Simplify the equation.
This simplifies to:
[tex]\[y = -2\][/tex]
Step 5: Write down the solution.
So, the solution to the equation [tex]\(2x + y = 0\)[/tex] when choosing [tex]\(x = 1\)[/tex] is:
[tex]\[x = 1 \][/tex]
[tex]\[y = -2\][/tex]
Thus, one specific solution is:
[tex]\((x, y) = (1, -2)\)[/tex]
