Hello there!
A. We have two lines: y = 2-x and y = 4x+3
Given two simultaneous equations that are both required to be true.. the
solution is the points where the lines cross... Which is where the two
equations are equal.. Thus the solution that works for both equations is
when
2-x = 4x+3
because where that is true is where the two lines will cross and that is the common point that satisfies both equations.
B. 2-x = 4x+3
x 2-x 4x+3
-3 5 -9
-2 4 -5
-1 3 -1
0 2 3
1 1 7
2 0 11
3 -1 15
The table shows that none of the integers from [-3,3] work because in no case does
2-x = 4x+3
To find the solution we need to rearrange the equation to the form x=n
2-x = 4x+3
2 -x + x = 4x + x +3
2 = 5x + 3
2-3 = 5x +3-3
5x = -1
x = -1/5
The only point that satisfies both equations is where x = -1/5
Find y: y = 2-x = 2 - (-1/5) = 2 + 1/5 = 10/5 + 1/5 = 11/5
Verify we get the same in the other equation
y = 4x + 3 = 4(-1/5) + 3 = -4/5 + 15/5 = 11/5
Thus the only actual solution, being the point where the lines cross, is the point (-1/5, 11/5)
C. To solve graphically 2-x=4x+3
we would graph both lines... y = 2-x and y = 4x+3
The point on the graph where the lines cross is the solution to the system of equations ...
[It should be, as shown above, the point (-1/5, 11/5)]
To graph y = 2-x make a table....
We have already done this in part B
x 2-x x 4x+3
_ __
-1 3 -1 -1
0 2 0 3
1 1 1 7
Just graph the points on a Cartesian coordinate system and draw the
two lines. The solution is, as stated, the point where the two lines
cross on the graph.
I hope I helped!
I will still trying to see if I can solve them another way that might be clearer.
