Question

Which first step for solving the given system using substitution results in an equation without fractions?

[3x+y=9

15x-3y = 1

Solve for x in the first equation.

Solve for y in the first equation.

Solve for x in the second equation.

Solve for y in the second equation.

Answer 1

It's B (the one above is right)

Explanation:

Answer 2

Solve for y in the first equation.

Explanation:

Given

3x+y=9

15x-3y = 1

Required

Determine the first step to avoid fractions

From the list of given options, the option that best answered the question is to Solve for y in the first equation.

Solving for y will let you substitute the expression for y in the second equation

Going by that:- Solve for y in the first equation.

`3x + y = 9`

Subtract 3x from both sides

`3x - 3x + y = 9 - 3x`

`y = 9 - 3x`

Substitute 9 - 3x for y in the second equation

`15x - 3y = 1` becomes

`15x - 3(9 - 3x) = 1`

`15x - 27 + 9x = 1`

Collect like terms

`15x + 9x = 1 + 27`

`24x = 28`

Divide both sides by 24

`(24x)/(24) = (28)/(24)`

`x = (28)/(24)`

Divide numerator and denominator by 4

`x = (7)/(6)`

Substitute 7/6 for x in the
`y = 9 - 3x`

`y = 9 - 3 * (7)/(6)`

`y = 9 - (7)/(2)`

Solve fraction

`y = (18-7)/(2)`

`y = (11)/(2)`