Answer:
A) The solution is x = 2 and y = 2
B) The graphs would intersect at the point (2, 2).
Step-by-step explanation:
A)
We start with the system of equations:
y = 6*x - 10
y = 2*x - 2
To solve this, the first step is to isolate one of the variables in one of the equations.
Here we can see that the variable "y" is already isolated in both equations, so we can skip that step.
Now we can "replace" the "y" in one of the equations for the correspondent expression in the other.
we can write:
(6*x - 10) = y
and for the second equation, we know that y = 2*x - 2
So replacing that, we get:
6*x - 10 = 2*x - 2
Now we can solve this for x.
6*x - 2*x = - 2 + 10
4*x = 8
x = 8/4 = 2
Now to find the value of y, we can just input this value of x in any one of the two equations:
y = 6*2 - 10 = 12 - 10 = 2
y = 2*2 - 2 = 4 - 2 = 2
So the solution of the system is:
x = 2, y = 2
B) Because the solution of the system is the ordered pair (2, 2), this means that the ordered pair belongs to the graph of both lines, then we can conclude that these lines will intersect at that point (the one that is common to both lines). Actually, when we have a system of equations, graphing both equations and finding the points where the graphs intersect is one method to estimate the solution of the system.
