Using algebra, find the solution to the system of inequalities

eliaskidszs

eliaskidszs

Answered question

2021-12-20

Using algebra, find the solution to the system of inequalities below
y53x
y+19x28x

Answer & Explanation

Jonathan Burroughs

Jonathan Burroughs

Beginner2021-12-21Added 37 answers

Step 1
Given, y53x,y+19x28x
Step 2
y+1919x28x19 [Subtract by 19]
yx28x19
x28x19y
So, x28x19y53x
x28x195+3x53x5+3x [Subtract 5 and add 3x]
x28x+3x240
x(x8)+3(x8)0
(x+3)(x8)0
Step 3
The region is possible when (x+3)0,(x8)0x3 and x8
So, 3x8. In interval notation, x[3,8]
Step 4
Now, (3)(3)3x(3)8 [Multiply by -3]
93x24
243x9
52453x5+9 [Add 5]
19y14
In interval notation, y[19,14]
Step 5
Hence, the solution of system of inequalities is x[3,8],y[19,14].
Becky Harrison

Becky Harrison

Beginner2021-12-22Added 40 answers

Step 1
Given: y53x (1)
y+19x8x (2)
Step 2
Simplify the equation (2)
y+19x8x
y+197x
y7x19
y(7x+19)
y7x+19 (3)
Step 3
Add equation (1) and (3)
04x+24
244x
4x24
x6
Step 4
Put the value of x in equation (3)
y7(6)+19
y23
y23
Step 5
Answer: {(x,y)R2x6,y23}
nick1337

nick1337

Expert2021-12-28Added 777 answers

Step 1
Given the system of inequalities
y53x
y+19x28x
Simplify the inequality y+19x28x as,
y+19x28x
yx28x19
x28x1953x
x28x19+3x53x+3x
x25x195
x25x240
(x+3)(x8)0
3x8
Step 2
Simplify the inequality y53x as,
y53x
53xy
3xy5
xy+53
Thus, 3x8
Since 3x8obtain the inequality for y as,
y+538 and y+533
y19 and y14y14
Thus,19y14
Therefore, the solution is 3x8 and 19y14

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