Question

how many solutions does the system of equations have? now that we have an equation with just one variable, x, we can perform balanced moves to try to isolate x to see if there is a value for x that will make the equation true. since there are x terms on both sides of the equation, lets get rid of the x term from one of the sides. what move can you make to get rid of the x term on the left side of the equation, 3x, while keeping the equation balanced? \\(\

$$\begin{cases} y = 3x + 6 \\\\ y = 3x + 3 \\end{cases}$$

\\) \\(3x + 6 = 3x + 3\\) options: add 3x to each side, subtract 3x from each side, multiply each side by 3x

Explanation:

Step1: Recall equation balancing rules

To eliminate the \(3x\) term from the left side (\(3x + 6\)) while keeping the equation \(3x + 6 = 3x + 3\) balanced, we use the inverse operation of the term we want to remove. The term is \(3x\), so we subtract \(3x\) from both sides.

• If we add \(3x\), we get \(3x+3x + 6=3x + 3x+ 3\) or \(6x + 6=6x + 3\), which doesn't eliminate \(x\).
• If we multiply by \(3x\), we get \(3x(3x + 6)=3x(3x + 3)\) or \(9x^{2}+18x = 9x^{2}+9x\), which complicates and doesn't eliminate \(x\).
• Subtracting \(3x\) from each side: \((3x + 6)-3x=(3x + 3)-3x\), simplifies to \(6 = 3\), which is false, but it's the correct move to eliminate \(x\) terms.

Answer:

Subtract 3x from each side