Lisa and Katie are playing a card game, and a total of 900 points has been scored. Lisa scored 150 more points than Katie. If you let l= the number of points that Lisa scored, and k= the number of points that Katie scored, then the problem can be represented by the system:
l+k=900 and l=k+150
Graph the system. How many points did each of them score?
250
To solve this system of equations graphically, we need to graph the two equations on a coordinate plane.
First, let's rewrite the equations in slope-intercept form:
l + k = 900
This equation can be rewritten as k = 900 - l.
l = k + 150
Now let's plot the two equations on a coordinate plane:
For the first equation k = 900 - l, we can start by assigning arbitrary values to l and then calculate the corresponding values of k. For example, if l = 0, then k = 900 - 0 = 900. If l = 200, then k = 900 - 200 = 700. If l = 400, then k = 900 - 400 = 500.
For the second equation l = k + 150, we can do the same thing. If k = 0, then l = 0 + 150 = 150. If k = 200, then l = 200 + 150 = 350. If k = 400, then l = 400 + 150 = 550.
Now let's plot the points (l, k) on the coordinate plane:
(l, k) = (0, 900), (200, 700), (400, 500), (550, 400), (700, 250), (850, 100)
Now we can draw a line passing through these points:
|
|
500 ------|------- /|
| |
| / |
| |
| / |
| |
| / |
| / |
| / |
| / |
|/________________|________
0 400 800
The solution to the system is the point of intersection between the two lines. From the graph, it appears that the point of intersection is approximately (550, 400).
Therefore, Lisa scored 550 points and Katie scored 400 points.
To solve this system of equations, we can use the method of substitution. Let's solve for one variable in terms of the other and then substitute that expression into the other equation.
From the equation l = k + 150, we can substitute l with k + 150 in the equation l + k = 900:
(k + 150) + k = 900
Combining like terms, we get:
2k + 150 = 900
Next, we can solve for k:
2k = 900 - 150
2k = 750
k = 375
Now that we have the value of k, we can substitute it back into the equation l = k + 150 to find l:
l = 375 + 150
l = 525
Therefore, Lisa scored 525 points, and Katie scored 375 points.
Cannot graph here. I will use substitution.
l = k + 150
l + k = 900
Substitute k+150 for l in the second equation and solve for k. Insert that value into the first equation to solve for l. Check by putting both values into the second equation.