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There is not a unique solution to this system of equations. It represents two parallel lines that do not intersect. Thus, there are no values of x and y that satisfy both equations simultaneously.
y =1/2x+2and y= -1/4x+8
To find the solution to this system of equations, you can set the two equations equal to each other:
1/2x + 2 = -1/4x + 8
To eliminate the fractions, you can multiply both sides of the equation by the least common multiple of the denominators, which is 4:
4(1/2x + 2) = 4(-1/4x + 8)
2x + 8 = -x + 32
Now, you can combine like terms:
2x + x = 32 - 8
3x = 24
Dividing both sides by 3:
x = 8
Now that you have the value of x, you can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = 1/2(8) + 2
y = 4 + 2
y = 6
Therefore, the solution to the system of equations is x = 8 and y = 6.
The solution to y=3 and x=-1
The solution to the equations y = 3 and x = -1 is x = -1 and y = 3.
Graph and then find the solution for y=3 and x=-1
To graph the equation y = 3, we can plot a single point on the y-axis at y = 3. Similarly, for x = -1, we plot a single point on the x-axis at x = -1. The solution to the system of equations is the point where the two graphs intersect.
Here is a graph showing the equation y = 3 plotted as a horizontal line at y = 3 and x = -1 plotted as a point on the x-axis:
```
| .
3 |______________________
| |
| |
| |
| |
| |
0|______________________
-1
```
As you can see, the point (-1, 3) represents the solution to the system of equations y = 3 and x = -1.
The solution to y=-1/2x-6 and y=7/6x+4
To find the solution to the system of equations y = -1/2x - 6 and y = 7/6x + 4, we can set the two equations equal to each other:
-1/2x - 6 = 7/6x + 4
To eliminate the fractions, we can multiply both sides of the equation by the least common multiple of the denominators, which is 6:
6(-1/2x - 6) = 6(7/6x + 4)
-3x - 36 = 7x + 24
To isolate the variable x, we can combine like terms by adding 3x to both sides and subtracting 24 from both sides:
-3x - 7x = 24 + 36
-10x = 60
Dividing both sides by -10:
x = -6
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
y = -1/2(-6) - 6
y = 3 - 6
y = -3
Therefore, the solution to the system of equations is x = -6 and y = -3.