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? \\(\

$$\begin{cases} y = 3x - 5 \\\\ y = -5 + 3x \\end{cases}$$

\\) \\(3x - 5 = -5 + 3x\\) options: add 3x to each side; multiply each side by 3x; subtract 3x from each side

Explanation:

To eliminate the \(3x\) term from the left side of the equation \(3x - 5=-5 + 3x\) while maintaining balance, we use the subtraction property of equality. Subtracting \(3x\) from both sides will cancel the \(3x\) on the left. Adding \(3x\) would introduce more \(x\)-terms, and multiplying by \(3x\) is unnecessary and would complicate the equation. So the correct move is to subtract \(3x\) from each side.

Answer:

Subtract 3x from each side