Answer:
y=x+10
y=-2x+1
(see attached picture)
Step-by-step explanation:
The idea of solving a system of equations graphically is taht both graphs cross each other at the same point.
The problem doesn't state so, but we can find the equations of the lines that pass through the desired point by using the point-slope form of the equation and by picking any slope we wish.
The slope-intercept form of a linear equation looks like this:
[tex]y-y_{1}=m(x-x_{1})[/tex]
so let's use the following slopes: [tex]m_{1}=1[/tex] and [tex]m_{2}=-2[/tex]. Remember, you can pick any slope you wish.
so now we can substitute the provided point (-3,7) and its respective slopes:
[tex]m_{1}=1[/tex]
y-7=1(x-(-3))
y=x+3+7
y=x+10
this will be our first equation.
[tex]m_{2}=-2[/tex]
y-7=-2(x+3)
y=-2x-6+7
y=-2x+1
so now we can plot the graphs of the given equations.
how to plot them? you can pick any x-value you like and use the provided equatioins to find the corresponding y-value. You plot the two points and build the graph.
Let's take the first equation:
y=x+10
and let's use the x-value x=0. We now substitute that into the equation so we get:
y=0+10
y=10
so now my two ordered pairs are (0,10) and (-3,7) so I can plot them on my graph and connect them with a straight line. (see attached picture.)
and we can follow the same procedure for the second graph.
let's use the x=0 again so we get:
y=-2(0)+1
y=1
so the ordered pairs are: (0,1) and (-3,7)
so we plot them to get our final graph (see attached picture)
Of course, this is one of the ways in which we can solve this problem. Since they are asking us to plot the graphs and not quite finding the equations for the system of equations, you could just draw any two lines you like and the answer would be correct as long as the two lines pass through the same point.
