Answer:
No solution.
Step-by-step explanation:
Given system of linear equations:
y=-1/2x + 4 and
x + 2y=-8.
Let us convert second equation in slope intercept form too.
x + 2y=-8
Subtracting x from both sides, we get
x -x+ 2y=-8-x
2y = -x-8
Dividing both sides by 2, we get
2y/2 = -x/2-8/2
y = -1/2 x - 4.
Let us find slope and y-intercept of each of the equation.
Slope-intercept form of a linear equation is y = mx+b, where m is the slope and b is y-intercept.
On comparing first equation y=-1/2x + 4 by slope-intercept form y = mx+b slope is -1/2 and y-intercept is 4.
For the second equation y = -1/2 x - 4 slope is -1/2 and y-intercept is -4.
Note: Slopes of both equations are same but y-intercepts are different.
So, the lines would be parallel and would not cut at any point.
So, the system of equation would not have any solution.
Therefore, correct option is 3rd option:
No solution.
