Let's answer these questions by solving the system by graphing.
y=-2x+8 & (I) y=4x+2 & (II)
To do this we will use a table of values. We will start with Equation 1.
x
y=-2x+8
y
(x,y)
-1
y=-2( -1)+8
10
( -1, 10)
0
y=-2( 0)+8
8
( 0, 8)
1
y=-2( 1)+8
6
( 1, 6)
Let's plot the points we found and connect them with a line.
Now, let's create a table of values for Equation 2.
x
y=4x+2
y
(x,y)
-1
y=4( -1)+2
-2
( -1, -2)
0
y=4( 0)+2
2
( 0, 2)
1
y=4( 1)+2
6
( 1, 6)
Using these points we can plot the second line.
We can see that lines intersect at (1,6). This means that the solution to the given system is x=1 and y=6. Now let's take a look at the question that does not belong to the other three.
If we consider one equation with two variables, we cannot find the exact solution to it. The only thing we can say about the solution to the equation with more than one variable is the relation between the variables. Let's consider Equation 1.
y=-2x+8
Here, the solution to this equation is any value of x and y, where y is equal to -2x+8. In other words, the solution is any point that lies on the line that represents the equation. We can think about Equation 2 in the same way.
y=4x+2
For this equation, the solution is any value of x and y such that y=4x+2. This means that the solution is any point that lies on the line representing this equation.
