Question

Y=x+1 and y=-x-3 in graphing,Substitution,and elemination

Answer 1

$\left\{\begin{array}{ccc}y=x+1\\y=-x-3\end{array}\right\\\\GRAPHING\ \text{(look at the picture)}\\\\y=x+1\\for\ x=0\to y=0+1=0\to(0,\ 1)\\for\ x=-1\to y=-1+1=0\to(-1,\ 0)\\\\y=-x-3\\for\ x=0\to y=-0-3=-3\to(0,\ -3)\\for\ x=-3\to y=-(-3)-3=0\to(-3,\ 0)\\\\Solution:\ (-2,\ -1)$

$SUBSTITUTION\\\\\left\{\begin{array}{ccc}y=x+1\\y=-x-3\end{array}\right\\\\\text{substitute}\ y=-x-3\ \text{to the first equation}\\\\-x-3=x+1\ \ \ \ |+3\\-x=x+4\ \ \ \ |-x\\-2x=4\ \ \ \ |:(-2)\\x=-2\\\\\text{substitute the value of x to the second equation}\\\\y=-(-2)-3=2-3=-1\\\\Solution:\ (-2,\ -1)$

$ELIMINATION\\\\\underline{+\left\{\begin{array}{ccc}y=x+1\\y=-x-3\end{array}\right}\ \ \ |\text{add both sides of the equations}\\.\ \ \ \ 2y=-2\ \ \ \ |:2\\.\ \ \ \ \ \ y=-1\\\\\text{put the value of y to the first equation}\\\\-1=x+1\ \ \ \ |-1\\x=-2\\\\Solution:\ (-2,\ -1)$