Answer:
The solutions of linear equations in the procedure
Explanation:
Part 1) we have
x+y=-1 ----> equation A
-6x+2y=14 ----> equation B
Solve the system by elimination
Multiply the equation A by 6 both sides
6*(x+y)=-1*6
6x+6y=-6 -----> equation C
Adds equation C and equation B
6x+6y=-6
-6x+2y=14
-------------------
6y+2y=-6+14
8y=8
y=1
Find the value of x
substitute in the equation A
x+y=-1 ------> x+1=-1 ------> x=-2
The solution is the point (-2,1)
Part 2) we have
-4x+y=-9 -----> equation A
5x+2y=3 ------> equation B
Solve the system by elimination
Multiply the equation A by -2 both sides
-2*(-4x+y)=-9*(-2)
8x-2y=18 ------> equation C
Adds equation B and equation C
5x+2y=3
8x-2y=18
----------------
5x+8x=3+18
13x=21
x=21/13
Find the value of y
substitute in the equation A
-4x+y=-9 ------> -4(21/13)+y=-9 ----> y=-9+84/13 -----> y=-33/13
The solution is the point (21/13,-33/13)
Part 3) we have
-x+2y=4 ------> equation A
-3x+6y=11 -----> equation B
Multiply the equation A by 3 both sides
3*(-x+2y)=4*3 ------> -3x+6y=12
so
Line A and Line B are parallel lines with different y-intercept
therefore
The system has no solution
Part 4) we have
x-2y=-5 -----> equation A
5x+3y=27 ----> equation B
Solve the system by elimination
Multiply the equation A by -5 both sides
-5*(x-2y)=-5*(-5)
-5x+10y=25 -----> equation C
Adds equation B and equation C
5x+3y=27
-5x+10y=25
-------------------
3y+10y=27+25
13y=52
y=4
Find the value of x
Substitute in the equation A
x-2y=-5 -----> x-2(4)=-5 -----> x=-5+8 ------> x=3
The solution is the point (3,4)
Part 5) we have
6x+3y=-6 ------> equation A
2x+y=-2 ------> equation B
Multiply the equation B by 3 both sides
3*(2x+y)=-2*3
6x+3y=6
so
Line A and Line B is the same line
therefore
The system has infinite solutions
Part 6) we have
-7x+y=1 ------> equation A
14x-7y=28 -----> equation B
Solve the system by elimination
Multiply the equation A by 7 both sides
7*(-7x+y)=1*7
-49x+7y=7 -----> equation C
Adds equation B and equation C
14x-7y=28
-49x+7y=7
------------------
14x-49x=28+7
-35x=35
x=-1
Find the value of y
substitute in the equation A
-7x+y=1 -----> -7(-1)+y=1 ----> y=1-7 ----> y=-6
The solution is the point (-1,-6)