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The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > = is -12. Hence, x + 4y -12
<h3>What is a System of Linear Inequalities?</h3>
A collection of linear inequalities in the same variables is referred to as a system of linear inequalities. Any ordered pair that fulfills all of the inequalities is the solution.
<h3>What is the calculation to prove the above assertion?</h3>Recall that:
- The linear equation with slope m and intercept c is given as follows.
y = mx + c
- The formula for slope of line with points and can be expressed as
m = (y2 - y1)/(x2 - x1)
Given that
The orange line intersects y-axis at (0,-2), therefore the y-intercept is -2.
The orange line intersect the points that are (1,0) and (0, -2).
The slope of the line can be obtained as follows:
m = (-2-0)/(0-1)
= -2/-1
= 2
The slope of the line is m = 2.
Therefore, the orange line is y 2x -2
The blue line intersects y-axis at (0,-3), therefore the y-intercept is -3.
The blue line intersect the points that are (-4, -2) and (0, -3)
The slope of the line can be obtained as follows.
m = (-3-(-2))/(0-(-4))
= (-3 + 2)/4
= - (1/4)
The slope of the line is:
m = -(1/4)
The inequalities is x + 4y b passes through the point (0, -3)
(0) + 4 (-3) = b
-12 =b
Thus, -12 in is the number that completes the system. Hence, x + 4y -12
Learn more about system of inequalities at;
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