solve these systems of equations. 5x-6y=21?

Question

solve these systems of equations and if a unique solution does not exist state weather the system is inconsistent of dependent

{5x-6y=21
{x-2y=5

Answer 1

Substitution Method

5x - 6y = 21- - - - - Equation 1
x - 2y = 5- - - - - - - Equation 2
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Isolate the x in eqjuation 2

x - 2y = 5

Transpose 2y

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

x = 2y + 5

Substitute the x value into equation 1
- - - - - - - - - -

5x - 6y = 21

5(2y + 5) - 6y = 21

The distributive property

10y + 25 - 6y = 21

Collect like terms

4y + 25 = 21

Transpose 25

4y + 25 - 25 = 21 - 25

Collect like terms

4y = - 4

Divide both sides of the equation by 4

4y / 4 = - 4 / 4

y = - 4/4

y = - 1

Substitute the y value into equation 2
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x - 2y = 5

x - 2(- 1) = 5

x - (- 2) = 5

x + 2 = 5

Transpose 2

x + 2 - 2 = 5 - 2

Collect like terms

x = 3

Substitute the x value into equation 2
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Check for equation 2

x - 2y = 5

3 - 2(- 1) = 5

3 - (- 2) = 5

3 + 2 = 5

5 = 5

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Check for equation 1

5x - 6y = 21

5(3) - 6(- 1) = 21

15 - (- 6) = 21

15 + 6 = 21

21 = 21

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Both equation balance

The solution set (3, - 1)

- - - - - - -s-

Answer 2

Multipy the first equation by ability of two and the 2d equation by ability of three. Now the first equation equals 10x-6y=-40. the 2d equation is 9x+6y=21. 9x+ 6y=21 upload them to remove y + 10x-6y=-40 and leave x. = 19x =-19 Divide by ability of 19. x=-a million Now change -a million for x in between the equations. 9x+6y=21 9(-a million)+6y=21 change -a million -9+6y=21 Multiply 6y=30 upload 9 to each and each side y=5 Divide by ability of 6 The device relies upon because it calls for both equations to be replied. Plus in case you're taking the unique equation (3x+2y=7) and plug contained in the solutions, you comprehend i'm properly!

Answer 3

1) 5x-6y=21
5x=21+6y

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

substituting 2) into 1)...

5(5+2y)=21+6y
25+10y=21+6y
10y-6y=21-25
4y=-4
y=-1

substituting y into 2)...
x=5+2y
x=5+2(-1)
x=5-2
x=3