We will graph the system of equations on one coordinate grid. Using the graph we will then solve the system. Let's start by graphing the parabola.
$x$ | $x_{2}+2x+1.5$ | $y$ |
---|---|---|
$-1.5$ | $(-1.5)_{2}+2(-1.5)+1.5$ | $0.75$ |
$-0.5$ | $(-0.5)_{2}+2(-0.5)+1.5$ | $0.75$ |
Both $(-1.5,0.75)$ and $(-0.5,0.75)$ are on the graph. Let's form the parabola by connecting these points and the vertex with a smooth curve.
Let's now graph the linear function on the same coordinate plane. For a linear equation written in slope-intercept form, we can identify its slope $m$ and $y$-intercept $b.$ $y=-x−1⇔y=-1x+(-1) $ The slope of the line is $-1$ and the $y$-intercept is $-3.$
We can see that our graph corresponds to option D.
Finally, let's try to identify the coordinates of the points of intersection of the parabola and the line.
We can see that the graphs do not intersect. Therefore, the given system of equations has no solutions.