solve the system: x- 6y = 11, 4x -7y = 10?

ANSWER: x=-1 and y=-2, or {(-1,-2)}

You can either use substitution or elimination to solve.
In this case, I think it's not too hard to use substitution.

If you add 6y to both sides of the first equation, x- 6y = 11 becomes
x = 11 + 6y

Substitute 11 + 6y for x in the second equation.
4(11+6y) - 7y = 10
44 + 24y - 7y = 10
44 + 17y = 10
17y = -34
y = -2

Plug this into either original equation to find x.
x - 6(-2) = 11
x - (-12) = 11
x +12 = 11
x = -1

or

4x - 7(-2) = 10
4x + 14 = 10
4x = -4
x = -1

y in terms of x, 1st & 2nd equations:
x - 6y = 11
y = (x - 11)/6

4x - 7y = 10
y = (4x - 10)/7

Value of x:
7(x - 11) = 6(4x - 10)
7x - 77 = 24x - 60
17x = - 17
x = - 1

Value of y (basing from last line of the 1st equation):
= (- 1 - 11)/6
= - 12/6 or - 2

Answer: x = - 1, y = - 2

Proof (2nd equation, substitute values of x & y):
4(- 1) - 7(- 2) = 10
- 4 + 14 = 10
10 = 10

x - 6y = 11 4x - 7y = 10 x = 11 + 6y x = 10/4 + 7y/4 11 + 6y = 10/4 + 7y/4 /.4 40 4 + 24y = 10 + 7y /-24y-10 34 = - 17y //17 y = -2 4x - 7y = 10 4x + 14 = 10 x = -a million x - 6y = 11 -a million + 12 = 11 y = -2 x = -a million

- 4x + 24 y = - 44
4 x - 7 y = 10-------------ADD

17 y = - 34
y = - 2

x + 12 = 11
x = - 1

x = - 1 , y = - 2

x - 6y = 11 (solve by using substitution)
4x - 7y = 10

x - 6y = 11
x = 6y + 11

4x - 7y = 10
4(6y + 11) - 7y = 10
24y + 44 - 7y = 10
24y - 7y = 10 - 44
17y = -34
y = -34/17
y = -2

x - 6y = 11
x - 6(-2) = 11
x + 12 = 11
x = 11 - 12
x = -1

∴ x = -1, y = -2

the answer by 1234 is exactly how I would figure it out.

you can use either substitution or elimination to solve this
SUBSTITUTION:

manipulate the first equation for x
x - 6y = 11
x = 11 + 6y
now substitute your x value into the second equation

4x - 7y = 10
4(11 + 6y) - 7y = 10
44 + 24y - 7y = 10
44 +17y = 10
17y = 10 - 44
y =- 2

now substitute your y value back into your first equation
x - 6y = 11
x - 6(-2) = 11
x + 12 = 11
x = -1

therefore x=-1 and y=-2

ELIMINATION:
In this, you have to make your x value in one equation equal your x value in the second equation...
4(x-6y=11)
4x-24y=44
now, subtract the two equations from each other..
(4x-24y=44) - (4x-7y=10)
-17y = 34
y = -2
now sub that into your second equation...
4x-7(-2)=10
4x+14=10
4x=-4
x=-1

therefore x=-1 and y=-2

CHECK :
you can check your answer is correct by subbing in your x and y values into each equation...
-1 - 6(-2) = 11
-1 + 12=11
11=11

4(-1) - 7(-2) = 10
-4 + 14 = 10
10 = 10

x- 6y = 11 ... (1); 4x -7y = 10 ... (2)
4 *(1) - (2) => -17y = 34 => y = -2, x = -1.

1 -6 11=>4 -24 44
-) 4 -7 10
----------------------------------------
-14 34
y=-34/14=-17/7
4x=10-17=-7
x=-7/4