Solve the system of equations by the substitution method.?

Question

{x - 5y = 3
{9x - 6y = 51

a. (6, 3)
b. (-7, 3)
c. (7, 2)
d. no solution

Answer 1

Solve the first equation for x. You get:
x = 5y + 3

Substitute the value of x from the first equation to the second one:
9(5y + 3) - 6y = 51
45y + 27 - 6y = 51
39y = 24
y = 24 / 39
y = 8/13

from here you see that there is no answer. The equation has a solution, but the solution is not in the choices you have.

it would be:
x = 40/13 + 3 = 40/13 + 39/13 = 79/13

x= 79/13
y = 8 / 13

Answer 2

Substitution Method

x - 5y = 3- - - - - -Equation 1
9x - 6y = 51- - - -Equation 2
- - - - - - - - -

Isolate the x in equation 1

x - 5y = 3

x - 5y + 5y = 5y + 3

Collect like terms

x = 5y + 3

Substitute the x value into equation 2
- - - - - - - - - - - - -

9x - 6y = 51

9(5y + 3) - 6y = 51

The distributive property

45y + 27 - 6y = 51

Collect like terms

39y + 27 = 51

Transpose 27

39y + 27 - 27 = 51 - 27

Collect like terms

39y = 24

Divide both sides of the equation by 39

39y / 39 = 24 / 39

y = 24/39

Simplify

y = 8 / 13

Substitute thy y value into equation 1
- - - - - - - - -

x - 5y = 3

x - 5(8/13) = 3

x - 40 / 13 = 3

Transpose 40/13

x - 40/13 + 40/13 = 3 + 40/13

Collect like terms

x = 39/13 + 40/13

x = 79/13

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

Check for equation 1

x - 5y = 3

79/13 - 5(8/13) = 3

79/13 - 40/13 = 3

39/13 = 3

3 = 3
- - - - - - - - - - -

Check for equatiion 2

9x - 6y = 51

9(79/13) - 6(8/13) = 51

711/13 - 48/13 = 51

663 / `13 = 51

51 = 51

- - - - - - - - -

Both equations balance

The solution set (79/13, 8/13)

- - - - - - - - - - s-

Answer 3

Multiply first eq by 9 and then subtract from second.
9x-9x-6y+45y=51-27=24
so 39y=24 y=8/13 so x=39/13+40/13
=79/13

check
9x-6y=51 works but not in the choices given.

Answer 4

x = 3+5y



2nd equation is

9x - 6y = 51
9(3+5y)-6y=51

27+45y-6y=51
27+39y=51
39y=24
y=24/39
= 8/13

Answer 5

the given simultaneous equation is INCONSISTENT, hence no solution. any of the methods used in solving S E will yield the same answer. you can try it yourself. the simplest approach being matrix method. it shows that x=3.5, y=0.6 plugging this into the original equation DOES not equate the right hand side.

Answer 6

D is tha right one cuz the answer will be a fraction which cannot be divided.