math question?

Question

Solve the system by substitution.
7x + 6y = 6
-4x - 4y = -4


I came up with (0,2)
Do you multiply 7x6=42 subtract 36 = 6-4 =2?

Answer 1

4x + 4y = 4
x + y = 1
x = 1 - y
7(1 - y) + 6y = 6
7 - 7y + 6y = 6
- y = - 1
y = 1
x = 0
Which agrees with your solution.

Answer 2

I'm afraid that you made a mistake with your method (which wasn't "substitution"). The answer is (x, y) = (0, 1).

You were asked to solve the system by SUBSTITUTION, so let's do it that way, first. (### --- see footnote.)

It's best to substitute from the SIMPLEST equation; that way, you're likely to make fewer mistakes.

The simplest equation is the second one. It's completely equivalent to

x + y = 1, so that y = 1 - x. ......(A)

Then, substituting for y from that, the first equation gives us:

7x + 6(1 - x) = 6, that is x = 0. Then from eqn. (A), y = 1.

Hence it's (x, y) = (0, 1).

[You'll notice how very few lines of work this approach requires.]

Live long and prosper.

### Although substitution worked well in this case, I generally favour working with addition or subtraction of whole equations. (I've noticed that fewer mistakes are made by students doing that.)

Rewrite the eqns. as:

7x + 6y = 6, and
-6x - 6y = -6.

Add them: x = 0. (You can't be much quicker than that!)

Then from the first one, y = 1.

Answer 3

Take the 1st equation,
6y = 6 - 7x
y = 1/6 (6 - 7x)

Substitute y in the 2nd equation,
-4x - 2/3 (6 - 7x) = -4
-4x - 4 + 14x/3 = -4
2x = 0
x = 0

y = 1/6 (6 - 0)
y = 1

(0, 1) is the solution

Answer 4

7x+6y=6------------------------(1)
also -4x-4y=-4
or 4x+4y=4
or x+y=1--------------------------(2)
or x=1-y,putting this value in (1),we have
7(1-y)+6y=6
or 7-7y+6y=6
or -y=6-7=-1 or y=1
also from (2),we have
y=1-x,putting this value in (2),we have
7x+6(1-x)=6
or 7x+6-6x=6
or x=6-6=0,so x=0 & y=1 ans

Answer 5

Answer is (0,1)