What are the coordinates of a point if the equation is -3x-3y=3 and y=-5x-17?
What are the coordinates of a point if the equation is -3x-3y=3 and y=-5x-17 ?
$$\begin{array}{lrcrr|}
\hline
(1) & y &=&\textcolor[rgb]{1,0,0}{ -5x-17 }&\\
\hline
(2) & -3x-3y &=& 3 &\qquad | \quad :(-3)\quad \\
(2) & x+y &=& -1 &\\
(1) \text{ in } (2) & x+\textcolor[rgb]{1,0,0}{(-5x-17)} &=& -1 & \\
& x-5x-17 &=& - 1 & \\
& -4x-17 &=& -1 & \qquad | \quad *(-1)\quad \\
& 4x+17 &=& 1 & \\
& 4x+17 &=& 1 & \qquad | \quad -17 \quad \\
& 4x &=& 1-17 & \\
& 4x &=& -16 & \\
& 4x &=& -16 & \qquad | \quad :4 \quad \\
& x &=& -4 &\\
\hline
\text{ in } (2) & -4+y &=& -1 & \qquad | \quad +4 \quad \\
& y &=& -1+4 & \\
& y &=& 3 &\\
\hline
\end{array}$$
x = -4 and y = 3
What are the coordinates of a point if the equation is -3x-3y=3 and y=-5x-17 ?
$$\begin{array}{lrcrr|}
\hline
(1) & y &=&\textcolor[rgb]{1,0,0}{ -5x-17 }&\\
\hline
(2) & -3x-3y &=& 3 &\qquad | \quad :(-3)\quad \\
(2) & x+y &=& -1 &\\
(1) \text{ in } (2) & x+\textcolor[rgb]{1,0,0}{(-5x-17)} &=& -1 & \\
& x-5x-17 &=& - 1 & \\
& -4x-17 &=& -1 & \qquad | \quad *(-1)\quad \\
& 4x+17 &=& 1 & \\
& 4x+17 &=& 1 & \qquad | \quad -17 \quad \\
& 4x &=& 1-17 & \\
& 4x &=& -16 & \\
& 4x &=& -16 & \qquad | \quad :4 \quad \\
& x &=& -4 &\\
\hline
\text{ in } (2) & -4+y &=& -1 & \qquad | \quad +4 \quad \\
& y &=& -1+4 & \\
& y &=& 3 &\\
\hline
\end{array}$$
x = -4 and y = 3