Question

Select the choice below that could be the first step in solving the following system of equations using substitution: -x + 6y − 10 = 0, 3x − 6y = 1
a. Replace the right side of the second equation with the first equation
b. Write the first equation in terms of x
c. Multiply the second equation by 3
d. Multiply the first equation by 3

Answer 1

where's the choices?

Answer 2

the first step would be to rearrange one of the equations into y=ax+b
so lets use the second one because it is easier
3x - 6y = 1
3x - 1 = 6y
6y = 3x -1
y = 3/6x - 1/6
y = 1/2x - 1/6

Answer 3

I would say B. Write the first equation in terms of x
But that would really mean you solved for y in the second equation.

3x-6y=1
-6y=1-3x
y=-1/6+ (-3/-6) x
y=-1/6 +1/2 x
OR you can rewrite this as
y=(1/2)x - (1/6)

So then you can replace y in the first equation by this
Equation 1: -x + 6y − 10 = 0
-x + 6{(1/2)x - (1/6)} -10 = 0
Now your first equation is only in terms of x.

Answer 4

Actually I changed my mind. Option d. makes the most sense.

Option a) doesn't make sense because in order to replace right side of the second equation with the first equation we would have to have
( Equation 1 Left hand side)= 1 (right hand side)

Option c: if you carried out this operation multiplying the second equation by 3 it would really be redundant it would not get you anywhere you simply wasted time making an equivalent equation by a factor of 3

Option b doesn't make sense b/c like I said before, you would really have to do another step before Option b is possible.

And finally option d is the one that would make the most sense b/c if you multiply the first equation by 3 you will get:
New Equation 1: -3x+18y-30=0 Rewrite it as
-3x+18y=30

And you will have Equation 2:
3x − 6y = 1
And now you can add New Equation 1 with Equation 2 and eliminate the x variable and you'll get 12y=31 and you can solve for y=31/12 and then you would go on and
substitute this value in equation 1, New equation 1 or equation 2 to solve for x.

Answer 5

thank you:)

Answer 6

you're welcome. any more questions? Or any part you would like to get more explanation? if not have fun with your studies :-)