how would I do this problem?

Question

I need to figure out how to do this but im clueless.. please help

I new to solve systems using substition.

1) -2x - 5y =7
7x + y = -8

and

2) x + 2y = 1
2x + 3y = -23

Answer 1

- 2x - 5y = 7- - - - - -Equation 1
7x + y = - 8- - - - - --Equation 2
- - - - - - - - -

Substitute method equation 2

7x + y = - 8

7x + y - 7x = - 7x - 8

y = - 7x - 8

Insert the y value into euation 1

- - - - - - - - - - - - - - - - - - - - - - - -

- 2x - 5y = 7

- 2x - 5(- 7x - 8) = 7

- 2x - (- 35 - 40) = 7

- 2x+ 35x + 40 = 7

33x + 40 = 7

33x + 40 - 40 = 7 - 40

33x = - 33

33x / 33 = - 33 / 33

x = - 33 / 33

x = - 1

Insert the x value into equation 1

- - - - - - - - - - - - - - - - - - - - - - - -

- 2x - 5y = 7

- 2(- 1) - 5y = 7

- (-2) - 5y = 7

2 - 5y = 7

2 - 5y - 2 = 7 - 2

- 5y = 5

- 5y / - 5 = 5 /- 5

y = - 5/5

y = - 1

Insert the y value into equatio 1

- - - - - - - - - - - - - - - - - - - - - - - -

Check for equation 1

- 2x - 5y = 7

- 2(- 1) - 5(- 1) = 7

- (- 2) - (- 5) = 7

2 + 5 = 7

7 = 7

- - - - - - - - - - - -

Check for equation 2

7x + y = - 8

7(- 1) + (- 1) = - 8

- 7 - 1= - 8

-8 = -8

- - - - - - - -

The solution set { -1, - 1 }

- - - - - - - - -s-

Answer 2

(1) -2x -5y = 7 & 7x+ y = -8 . From the 2nd equation find the value of y , we get y = -7x -8 now put this value in the 1st equation .We get,

-2x - 5( -7x - 8) = 7 or -2x + 35x + 40 = 7 or 33x = -33 or x = -1 Now substitute the value of x in y .to get the value of y ,

We get x= -1 and y = -1

(2) Find the value of x from the 1st equstion .We get x = -2y +1 .Now substitute the value in the equation 2nd we get

2( -2y +1) +3y= -23 or -4y +2 + 3y = -23 or -y = -25 or y=25 & x= -49

Answer 3

1)
-2x - 5y = 7 (1)
7x + y = -8 (2)

Multiply (2) by 5
35x + 5y = -40 (3)

Now add (1) to (3)
35x + 5y + (-2x - 5y) = -40 + 7
35x + 5y - 2x - 5y = -33
33x = -33
x = -1

Put x =-1 back into equation (2)
(7 * -1) + y = -8
-7 + y = -8
(Add 7 to both sides)
y = -1

Both y and x = -1

2)
x + 2y = 1 (1)
2x + 3y = -23 (2)

Multiply (1) by 2
2x + 4y = 2 (3)

Subtract (2) from (3)
2x + 4y - (2x + 3y) = 2 - - 23
2x + 4y -2x - 3y = 25
y = 25

Sub y=25 back into (1)

x + 2y = 1
x + 50 = 1
Take 50 from both sides
x = -49

Answer 4

Take 2nd equation and isolate y:

y=-7x-8

Now 1st equation can take form:

-2x-5(-7x-8)=7

-2x+35x+40=7

33x = -33

x= -1 so: -7+y= -8 y= -1

2) x=1-2y

2(1-2y) + 3y = -23

2-4y+3y = -23
-y= -25
y=25 so: x+ 50 = 1 x= -49

Answer 5

solve one of the equations for one variable. for the first one problem, second part, if you subtract 7x from both sides, you end up with y=-8 -7x

now, every time you see a y, write (-8 -7x) instead. when you plug that into the first part of the first question.
-2x -5(-8 -7x) = 7
-2x +40 +35x = 7
33x = -33
x = -1

now that you know what x is, plug in (-1) for x, and solve for y
y = -1

Answer 6

1) Multiply the second by 5
-2x - 5y =7
35x +5 y = -40
add them term by term
33x=-33
divide by 33
x=-1
y=-1
2)
multiply the first by -2
-2x-4y=-2
2x+3y=-23
by adding
-y=-25
y=25
x=-49

Answer 7

Ill help with first, second will follow same pattern

with a view to eliminating y multiply second eqn by 5 (in general case you would multiply first by one factor, and second by another, to get same y coefficient)
-2x -5y = 7
35x + 5y = -40
add them
33x = -33
so x=-1
substitute back
+2 - 5y = 7
so 5y = -5
so y = -1 as well