Question

How would you solve these systems? I'm in need help!! Thanks so much!

1. -7x-6y=-21
-x-6y=-3

2. -7x+2y=13
-14x+4y=26

3. 2x+10y=30
-10x-6y=-18

Answer 1

For -7x-6y=-21
Simplifying
-7x + -6y = -21

Solving
-7x + -6y = -21

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '6y' to each side of the equation.
-7x + -6y + 6y = -21 + 6y

Combine like terms: -6y + 6y = 0
-7x + 0 = -21 + 6y
-7x = -21 + 6y

Divide each side by '-7'.
x = 3 + -0.8571428571y

Simplifying
x = 3 + -0.8571428571y

Answer 2

You would use the same technique for the other ones, also.

Answer 3

for all 3 , elimination looks like the easiest way

1.
-7x-6y=-21
-x-6y=-3
subtract them to eliminate the y's
-6x = -18
x = 3
back into the 2nd:
-3-6y=-3
-6y=0
y = 0 ----------> x = 3, y = 0

2.
-7x+2y=13
-14x+4y=26
Did you notice that the 2nd equation is simply twice the first ?
So there is an infinite number of solutions, no unique solution

3.
2x+10y=30
-10x-6y=-18

first one times 5 ---> 10x + 20y = 60
write down the 2nd --> -10x - 6y = -18
add them:
14y = 42
y = 3

back into the first:
2x + 30 = 30
2x = 0
x=0