Question

find the solution of the system of equations. answer with the solution, or with \all real numbers\ if there are infinite solutions, or with
o solution\ if there are no solutions.\

$$\begin{cases} 3x - 3y = -3 \\\\ 9x - 9y = 4 \\end{cases}$$

Explanation:

Step1: Simplify the first equation

Divide the first equation \(3x - 3y=-3\) by 3. We get \(x - y=-1\), which can be rewritten as \(x - y=-1\) or \(3(x - y)=-3\) (multiplying both sides by 3 gives \(3x - 3y=-3\), which is consistent).

Step2: Analyze the second equation

The second equation is \(9x - 9y = 4\). We can factor out 9 from the left - hand side, getting \(9(x - y)=4\). From the first equation, we know that \(x - y=-1\). Substitute \(x - y=-1\) into the left - hand side of the second equation: \(9\times(-1)=-9
eq4\).
This means that the two equations represent parallel lines (since they have the same slope, as the coefficients of \(x\) and \(y\) are proportional, but the constant terms are not in the same proportion), and there is no point that lies on both lines.

Answer:

no solution