Solve the systems using substitution?

Question

1) 6x + 2y = -2
4x + y = 1

2) 3x + 2y = 6
x + 2y = -6

3) 5x - 4y = 9
x - 2y = -3

4) x + 3y = 5
4x + 5y = 13

5) x + 3y = 8
2x - y = 9

Answer 1

1) 6x + 2y = -2 equation (a)
4x + y = 1 equation (b)

Solve for y using equation (b)
y = 1 - 4x
Substitute y in equation (a)
6x + 2(1-4x) = -2
6x + 2 -8x = -2
-2x = -4
x = 2
Substitute x in equation (b)
4(2) + y = 1
8 + y =1
y = -7

2) 3x + 2y = 6 equation (a)
x + 2y = -6 equation (b)

Solve for x in equation (b)
x = -6 - 2y
Substitute x in equation (a)
3(-6 - 2y) + 2y = 6
-18 - 6y + 2y = 6
-18 -4y = 6
-4y = 24
y = -6
Substitute the value of y in equation (b)
x + 2(-6) = -6
x - 12 = -6
x = 6

3) 5x - 4y = 9 equation (a)
x - 2y = -3 equation (b)

Solve for x using equation (b)
x = 2y -3
Substitute x in equation (a)
5(2y-3) - 4y =9
10y -15 -4y = 9
6y - 15 = 9
6y = 24
y = 4
Substitute the value of y in equation (b)
x - 2(4) = -3
x - 8 = -3
x = 5

4) x + 3y = 5 equation (a)
4x + 5y = 13 equation (b)

Solve for x using equation (a)
x = 5 -3y
Substitute x in equation (b)
4(5-3y) + 5y = 13
20 - 12y + 5y = 13
20 -7y = 13
-7y = -7
y = 1
Substitute the value of y in equation (a)
x + 3(1) = 5
x + 3 = 5
x = 2

5) x + 3y = 8 equation (a)
2x - y = 9 equation (b)

Solve for x using equation (a)
x = 8 - 3y
Substitute x in equation (b)
2(8-3y) -y = 9
16 - 6y - y = 9
16 - 7y = 9
-7y = -7
y = 1
Substitute the value of y in equation (a)
x + 3y = 8
x + 3(1) = 8
x + 3 = 8
x = 5

Answer 2

1) 6x + 2y = -2 => y = 1 - 4x
=> 6x + 2y= -2 <=> 6x + 2(1 - 4x)= -2 <=> 6x + 2 - 8x = -2 <=> -2x = -4 => x=2 => y= -7

2) x + 2y = -6 => x= -6 - 2y
=> 3x + 2y = 6 <=> 3(-6 - 2y)+2y=6 <=> -18 - 6y+2y= 6 <=> -4y= 24 <=> y= -4 <=> x= -6+8= -2

3) x - 2y = -3 <=> x = 2y - 3
5x - 4y = 9 <=> 5(2y - 3) - 4y=9 <=> 10y - 15 - 4y=9 <=> 6y = 24 <=> y=4 <=> x=5

4) x + 3y = 5 <=> x=5-3y
4x + 5y = 13 <=> 4(5-3y)+5y = 13 <=> 20 - 12y +5y = 13 <=> -7y = -7 <=> y= -1 <=> x = 8

And the last one...

5) x + 3y = 8 <=> x=8 - 3y
2x - y = 9 <=> 2(8 - 3y) - y = 9 <=> 16 - 6y - y = 9 <=> -7y = -7 <=> y = -1 <=> x = 11

Hope you got it! :)

Answer 3

Substitution Method

1).

6x + 2y = - 2- - - - -Equation 1
4x + y = 1- - - - - - -Equation 2
- - - - - - - - - - -

Isolate y in equation 2

4x + y = 1

Transpose 4x

4x + y - 4x = - 4x + 1

y = - 4x + 1

Substitute the y value into equation 1
- - - - - - - - - - -

6x + 2y = - 2

6x + 2( - 4x + 1) = - 2

Distributive property

6x + ( - 8x + 2) = - 2

Remove parenthesis

6x - 8x + 2 = - 2

Collect like terms

- 2x + 2 = - 2

Transpose 2

- 2x + 2 - 2 = - 2 - 2

Collect like tems

- 2x = - 4

Divide both sides of the equation by - 2

- 2x / - 2 = - 4 / - 2

x = - 4 / - 2

x = 2

Insert the x value into equation 2
- - - - - - - - - - - -

4x + y = 1

4(2) + y = 1

8 + y = 1

Transpose 8

8 + y - 8 = 1 - 8

Collect like terms

y = - 7

Insert the y value into equation 2
- - - - - - - - - - -

Check for equation 2

4x + y = 1

4(2) + ( - 7) = 1

8 - 7 = 1

1 = 1
- - - - - - - - -

Check for equation 1

6x + 2y = - 2

6(2) + 2( - 7) = - 2

12 + ( - 14) = - 2

12 - 14 = - 2

- 2 = - 2
- - - - - - - - - -

Both equations balance

The solution set is { 2, - 7 }

- - - - - - - - -s-

Answer 4

not confusing: 3x + 4y = -sixteen, 3x + 11 = y... or; 3x - y = -11 Subtract out the 2nd equation from the 1st. 5y = -5 y = -one million And now remedy for x: 3x + 4y = -sixteen, 3x + 11 = y 3x + (-4) = -sixteen, 3x + 11 = (-one million) 3x = -12, 3x = -12 x = -4, x = -4 y = -one million and x = -4 No mistaking it from the above. this is an ironclad info!