Explanation
Problem #2
We must find the solution to the following system of inequalities:
(1) We solve for y the first inequality:
Now, we multiply both sides of the inequality by (-1), this changes the signs on both sides and inverts the inequality symbol:
The solution to this inequality is the set of all the points (x, y) over the line:
This line has:
• slope m = 3/2,
,
• y-intercept b = -2.
(2) We solve for y the second inequality:
The solution to this inequality is the set of all the points (x, y) below the line:
This line has:
• slope m = -1/3,
,
• y-intercept b = 2.
(3) Plotting the lines of points (1) and (2), and painting the region:
• over the line from point (1),
,
• and below the line from point (2),
we get the following graph:
Answer
The points that satisfy both inequalities are given by the intersection of the blue and red regions:
One root belonged to an old tree next to the road, and the other is part of a small tree.
The point of intersection of the two lines is at (1,-1)
<h3>System of equation</h3>
The given system of expression is shown below
x - 2y = 3
5x + 3y = 2
The solution to the system of equation is the point of intersection
From equation 1
x = 3 + 2y
Substitute into 2
5(3+2y) + 3y = 2
15 +10y + 3y = 2
13y = -13
y = -1
Substitute y = -1 into 3
x = 3 + 2y
x = 3+(-2)
x = 1
Hence the point of intersection of the two lines is at (1,-1)
Learn more on system of equation here: brainly.com/question/25976025
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Call the two equations above A and B, in order to not confuse them.
A: -2x + 6y = -38
B: 3x - 4y = 32
For this system we have opposites in x and y, so Elimination (or Linear Combination) works best. Either variable works, so let's work with x first and multiply A by 3 and B by 2. This is done so we get opposites in A and B then when added together give zero.
-2x + 6y = -38 ------> multiply by 3 ----> -6x + 18y = -114
3x - 4y = 32 ------> multiply by 2 -----> 6x - 8y = 64
Now we add the new equations. The -6x and 6x are opposites and go away. We are left with
10y = -50. We divide both sides by 10 and get that y = -5.
Now we take y = -5 and put it into an original equation. Let's use A.
-2x + 6y = -38 the original equation A
-2x + 6(-5) = -38 we found y = -5
-2x + (-30) = -38 evaluating and multiplying
-2x - 30 = -38 apply the parentheses
-2x = -8 add 30 to both sides
x = 4 divide on both sides by -2
Thus x = 4 and y = -5, or (4, -5) is the solution.
