Determine the point at which these two lines intersect:
$\begin{array}{l}y=-x-3 \\ y=3 x\end{array}$

Answer

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Answer

The point of intersection of the two lines is $\boxed{\left(-\frac{3}{4}, -\frac{9}{4}\right)}$

Steps

Step 1 ：Set the two equations equal to each other: -x - 3 = 3x

Step 2 ：Solve for x to get $x = -\frac{3}{4}$

Step 3 ：Substitute $x = -\frac{3}{4}$ into either of the original equations to find the corresponding y-coordinate, which is $y = -\frac{9}{4}$

Step 4 ：The point of intersection of the two lines is $\boxed{\left(-\frac{3}{4}, -\frac{9}{4}\right)}$