Answer:
none
Explanation:
To determine which graph matches the given system of equations, we can first solve the system for x and y.
Starting with the system:
5x + 2y = 2
3x - 3y = 18
We can solve for x in terms of y by rearranging the first equation:
5x + 2y = 2
5x = 2 - 2y
x = (2 - 2y)/5
Then we can substitute this expression for x into the second equation:
3x - 3y = 18
3[(2 - 2y)/5] - 3y = 18
6 - 6y - 15y = 90
-21y = 84
y = -4
Now we can substitute this value of y into either equation to solve for x:
5x + 2y = 2
5x + 2(-4) = 2
5x = 10
x = 2
So the solution to the system is x = 2, y = -4.
To match this solution with one of the graphs, we can plot the points (2, -4) and see which graph passes through that point.
Looking at the answer choices:
a) A line includes points (0, 6) and (2, 4). This line has a slope of -1 and a y-intercept of 6, so it does not pass through the point (2, -4).
b) A line includes points (0, 2) and (-2, 7). This line has a slope of -2.5 and a y-intercept of 2, so it also does not pass through the point (2, -4).
c) A line includes points (0, 1) and (1, -4). This line has a slope of -5 and a y-intercept of 1, so it does not pass through the point (2, -4).
d) A line includes points (0, 6) and (1, 3). This line has a slope of -3 and a y-intercept of 6, so it also does not pass through the point (2, -4).
Therefore, none of the given graphs match the system of equations.