Answer:
<h3>No solution.</h3>
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.
<h3><em>Note: Slopes of both equations are same but y-intercepts are different.</em></h3><h3><em>So, the lines would be parallel and would not cut at any point.</em></h3><h3><em>So, the system of equation would not have any solution.</em></h3>
Therefore, correct option is 3rd option:
<h3>No solution.</h3>
