Answer
Option A is correct.
The approximate solution to this system of equations from the graph of the plots of the equation is (1.2, 3.4)
Step-by-step explanation
There are a couple of ways to solve systems of equations. Two out of the numerous ways is to calculate or use graphical methods.
- If you're calculating, you simply solve the simultaneous equation through any calculation means possible (elimination or substitution)
- If you're using graphical methods, you'll first need to plot the two or more equations, all on the same graph. The solution is then the point where the plot of the equations intersect or meet.
For this question, the system of equations is
y = -0.5x + 4
y = 1 + 2x
If one wanted to calculate, we would just substitute the value of y in the first equation into the second equation and have
-0.5x + 4 = 1 + 2x
1 + 2x = -0.5x + 4
2x + 0.5x = 4 - 1
2.5x = 3
Divide both sides by 2.5
(2.5x/2.5) = (3/2.5)
x = 1.2
Recall that y = -0.5x + 4
y = -0.5(1.2) + 4
y = -0.6 + 4 = 3.4
If the graph of the two plots was available, the two plots will intersect at
(1.2, 3.4), that is, x = 1.2 and y = 3.4
Since you've not uploaded the graph, I quickly made the plots on the same and will upload it now.
As we can see the point of intersection of the two plots corresponds with the answer we obtained from the calculation method.
Hope this Helps!!!