Solve the system.
$ \left\{ \begin{tabular}{l} $ y = x + {\color{red}-3} $ \\ $ y = -{\color{red}2} x + {\color{red}9} $ \end{tabular} \right. $
x =
y =
To solve this system of equations, we can set the two equations equal to each other and solve for the value of x.
$y = x - 3$ (equation 1)
$y = -2x + 9$ (equation 2)
Setting equation 1 equal to equation 2, we have:
$x - 3 = -2x + 9$
To isolate the variable x, we need to combine like terms:
$3x = 12$
Dividing both sides by 3, we obtain:
$x = 4$
To find the corresponding value of y, we substitute the value of x back into either equation. Using equation 1, we have:
$y = 4 - 3$
$y = 1$
Therefore, the solution to the system of equations is:
x = 4
y = 1