Answer:
x=2, y=7 -------> y=11-2x and 4x-3y=-13
x=5, y=2 ------> 2x+y=12 and x=9-2y
x=3, y=5 -----> 2x+y=11 and x-2y=-7
x=7, y=3 ------> x+3y=16 and 2x-y=11
Explanation:
Part 1) we have
2x+y=12 -----> equation A
x=9-2y -----> equation B
Solve by substitution
Substitute equation B in equation A and solve for y
2(9-2y)+y=12
18-4y+y=12
4y-y=18-12
3y=6
y=2
Find the value of x
x=9-2(2)=5
therefore
The solution is
x=5, y=2
Part 2) we have
x+2y=9 -----> equation A
2x+4y=20 ---> equation B
Multiply equation A by 2 both sides
2(x+2y)=9*2
2x+4y=18 -----> equation C
Compare equation C with equation B
Both equations have the same slope with different y-intercept
therefore
The lines are parallel and the system has no solution
Part 3) we have
x+3y=16 ------> equation A
2x-y=11 -----> equation B
Solve the system by elimination
Multiply equation B by 3 both sides
3(2x-y)=11*3
6x-3y=33 -----> equation C
Adds equation A and equation C
x+3y=16
6x-3y=33
----------------
x+6x=16+33
7x=49
x=7
Find the value of y
x+3y=16
7+3y=16
3y=16-7
3y=9
y=3
therefore
The solution is
x=7, y=3
Part 4) we have
y=11-2x -----> equation A
4x-3y=-13 ---> equation B
Solve by substitution
Substitute equation A in equation B and solve for x
4x-3(11-2x)=-13
4x-33+6x=-13
10x=-13+33
10x=20
x=2
Find the value of y
y=11-2(2)=7
therefore
The solution is
x=2, y=7
Part 5) we have
y=10+x -----> equation A
-3x+3y=30 ---> equation B
Multiply equation A by 3 both sides
3*y=3*(10+x)
3y=30+3x
Rewrite
-3x+3y=30 ----> equation C
equation B and equation C are identical
therefore
The system has infinitely solutions
Part 6) we have
2x+y=11 -----> equation A
x-2y=-7 ----> equation B
Solve by elimination
Multiply equation A by 2 both sides
2(2x+y)=11*2
4x+2y=22 ----> equation C
Adds equation B and equation C and solve for x
x-2y=-7
4x+2y=22
----------------
x+4x=-7+22
5x=15
x=3
Find the value of y
x-2y=-7
3-2y=-7
2y=3+7
2y=10
y=5
therefore
The solution is
x=3, y=5