Question

Solve the system of equations by the substitution method.

y=3x+1
3y-7x=9
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The solution is
(Simplify your answer. Type an ordered pair.)
OB. There are infinitely many solutions.
OC. There is no solution.

Answer 1

the solution is (3, 10 )

Explanation:

given the system of equations

y = 3x + 1 → (1)

3y - 7x = 9 → (2)

substitute y = 3x + 1 into (2)

3(3x + 1) - 7x = 9 ← distribute parenthesis on left side and simplify

9x + 3 - 7x = 9

2x + 3 = 9 ( subtract 3 from both sides )

2x = 6 ( divide both sides by 2 )

x = 3

substitute x = 3 into (1) and solve for y

y = 3(3) + 1 = 9 + 1 = 10

The solution is (3, 10 )