Answer:
1. x = -1 y= -2
2. infinitely many solutions
3. x = 6 y= -7
4.no solution
5. x = -3 y = -17
6. x= 3 y = 7
Explanation:
1) y=x-1
7x+6y= -19
6y= -19 -7x
y= (-7x-19)/6
since x-1 and (-7x-19)/6 are both equal to y they are equal to each other
this is how to get x
x-1 = (-7x-19)/6
6x-6 = -7x-19
13x = -13
x = -1
now put back -1 in the equation to get y
y=x-1
y = -1 -1
y= -2
2)-10x+2y=-12
y=5x-6
2y= -12 + 10x
y= -6 + 5x
y = 5x - 6
5x-6 = 5x - 6
0 = 0
when something is
equal to itself its
infinitely many solutions
(when something is not equal to something its no solution)
((when something is equal to just one answer its one solution)
3) y= -4x+17
y=x-13
-4x+17 = x-13
30 = 5x
x = 6
y=x-13
y=6-13
y= -7
4) -3x-15y=8
x+5y=5
-3x-15y=8 -> y = -1/15(3x-8)
5y=5-x -> y= 1/5 (5-x)
-1/15(3x-8) = 1/5 (5-x)
-x-8/3 = 5-x
0 = 23/3
(when something is not equal to something its no solution)
5) -3x+6y=-3
3x-y=8
-3x+6y= -3 -> y = 1/6(3x-3)
3x-y=8 -> y = 3x-8
1/6(3x-3) = 3x-8
3x-3 = 18x-48
x-1 = 6x - 16
5x = -15
x = -3
3x-y=8
3(-3)-y=8
-9-8 = y
y = -17
6) -6x+6y=24
-3x-8y=1
-6x+6y=24 -> y = 1/6(6x+24) -> y = x+4
-3x-8y=1 -> -3x-1 = 8y -> y = 1/8 (-3x-1)
1/8 (-3x-1) = x+4
-3x-1 = 8x+32
11x = 33
x= 3
-6x+6y=24
-6(3)+6y=24
-18 + 6y = 24
6y = 24 + 18
6y = 42
y = 7