Answer: To solve this system of equations, we need to find two points that satisfy both equations. We can then use these two points to graph the equations and find their point of intersection, which will be the solution to the system.
Let's start by finding some points that satisfy the second equation, y = |2x^2 - 5|:
When 2x^2 - 5 is positive, y = 2x^2 - 5
If we set x = 0, then y = |-5| = 5, so one point is (0, 5).
If we set x = 1, then y = |2 - 5| = 3, so another point is (1, 3).
When 2x^2 - 5 is negative, y = -(2x^2 - 5) = 5 - 2x^2
If we set x = 0, then y = 5, so another point is (0, 5).
If we set x = -1, then y = 5 - 2 = 3, so another point is (-1, 3).
Now we have four points that satisfy the second equation: (0, 5), (1, 3), (-1, 3), and (0, 5). We can use these points to graph the equation y = |2x^2 - 5|, as shown below:
|
5 -+ +------------*------+------------*------+--
| | |
4 -+ +--
| |
3 -+ +------------*------+------------*------+ |
| | |
2 -+ +--
| |
1 -+ +--
| |
+------------------------------------------------------+
-1 -0.5 0 0.5 1 1.5 2 2.5 3
Next, we need to find the points that satisfy the first equation, 3x + y = 0. One way to do this is to plug in values of x and solve for y:
If x = 0, then y = 0, so one point is (0, 0).
If x = 1, then y = -3, so another point is (1, -3).
Now we have two points that satisfy both equations: (0, 5) and (1, -3). We can use these points to graph the equations and find their point of intersection:
|
5 -+ +------------*------+------------*------+--
| | |
4 -+ +--
| |
3 -+ +------------*------+------------*------+ |
| | |
2 -+ +--
| |
1 -+ +--
| |
+------------------------------------------------------+
-1 -0.5 0 0.5 1 1.5 2 2.5 3
(0, 5)
/
__/_____
/ / \
/ / \
(-1.5, 0) / / (0,0) \ (1.5, 0)
\ / \ /
\/--------------*---------------> x
(-3/4, -9/4)
From the graph, we can see that the two equations intersect at approximately (-0.75, -2.25). Therefore, the solution to the
Explanation: