using the substituionmethod solve the system 2x+3y=-4 and then under thatg x-2y=5?

Answer 1

2x + 3y = -4
x-2y = 5

Write x as x= 5+2y
Sub this back in the first equation
2(5 + 2y) + 3y = -4

10 + 4y + 3y = -4
7y = -4 - 10 = -14
y = -2

x = 5 + 2y = 5 + (-4) = 1

Check this:
2x + 3y = -4
2(1) - 3(-2) = -4
2 - (6) = -4 Good!

Answer 2

2x + 3y = -4 and
x - 2y = 5. Solve by substitution?

x - 2y = 5 gives
x = 5 + 2y = 2y + 5 Now substitute 2y + 5 in the first equation

2(2y + 5) + 3 y = -4 Now simplify

4y + 10 + 3y = -4
4y + 3y = -4 - 10
7y = -14
y = -2 Now go back to the second equation and substitute -2 for y

x - 2(-2) = 5
x + 4 = 5
x = 5 - 4
x = 1

HTH

Charles

Answer 3

2x + 3y = - 4- - - - -Equation 1
x - 2y = 5- - - - - - -Equation 2
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Substitution Method equation 2

x - 2y = 5

x - 2y + 2y = 5 + 2y

x = 5 + 2y

The answer is x = 5 + 2y

Insert the x value into equation 1

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2x + 3y = - 4

2(5 + 2y) + 3y = - 4

10 + 4y + 3y = - 4

10 + 7y - 10 = - 4 - 10

7y = - 14

7y/7 = - 14/7

y = - 2

The answer is y = - 2

Insert the y value into equation 1

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2x + 3y = - 4

2x + 3(- 2) = - 4

2x + (- 6) = - 4

2x - 6 = - 4

2x - 6 + 6 = - 4 + 6

2x = 2

2x/2 = 2/2

x = 1

The answer is x = 1

Insert the x value into equation 1
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Check for equation 1

2x + 3y = - 4

2(1)+ 3(- 2) = - 4

2 + (- 6) = - 4

2 - 6 = - 4

- 4 = - 4

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Check for equation 2

x - 2y = 5

1 - 2(- 2) = 5

1 - (- 4) = 5

1 + 4 = 5

5 = 5

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The solution set is { 1, -2 }

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Answer 4

2x + 3y = 4
x - 2y = 5 solve for x ; x = 2y + 5

2( 2y + 5 ) + 3y = 4
4y + 10 + 3y = 4
7y + 10 =4
7y = - 6
y = - 6/7

if that is the value of y then x = 2(-6/7) +5
work that out and that is the value of x.

Using matrices is an easier method of solving systems.

Answer 5

First solve the second equation for x or y. I will solve for x

x-2y=5
x=5+2y because u added -2y to both sides.

Then substitute this equation into x for the first equation, like this.
2(5+2y)+3y= -4
10+4y+3y= -4
10+7y= -4
7y=-14
y= -2

You have now gotten the y answer. Now, you need to substitute the y answer into the equation to get the x answer.

x=5+2y
x=5+2(-2)
x=5-4
x=1

So your answers for the solution set are (1,-2)

Answer 6

by substitution it means y or x in one equation to be subtituted in the other equation.
lets say
2x+3y=-4---------------eqn 1
x-2y=5-------------------eqn 2

from eqn 2, x=5+2y ------eqn 2b
and since the x and the y in eqn 1 and 2 are the same, x in eqn 1 can be subtituted with the x in eqn 2b

2( 5+2y) + 3y= -4
10 +4y + 3y = -4
7y = -10 -4
7y = -14
y = -14/7
y = -2

from eqn 2b x= 5 + 2y and y = -2
therefore x = 5 + 2 (-2)
x = 5 - 4
x = 1

x=1 and y = -2

Answer 7

2x+3y=-4
x-2y=5=>x=5+2y
2(5+2y)+3y=-4=>10+4y+3y=-4=>7y=-14=>y=-2
x=5+2*(-2)=>x=1
hope this helps!

Answer 8

x = 1
y = -2