Question

Which number completes the system of linear

Answer 1

The number that completes the System of Linear Inequalities represented by the Graph y >= 2x – 2 and x + 4y > =  is -12. Hence, x + 4y $\geq$ -12

What is a System of Linear Inequalities?

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.

What is the calculation to prove the above assertion?

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 $\geq$ 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 $\geq$ 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 $\geq$ -12

Learn more about system of inequalities at;
brainly.com/question/9774970
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