Question

Solve the system by the substitution method x = 7y + 18 x = 2y + 7 What is the solution set of the system? Select the correct choice below and, if necessary, fill in the answer box to complete your answer. OA) Type an ordered pair) OB. There are infinitely many solutions ос. Трете is no solution

Answer 1

The system of equation:

x = 7y + 18 (1)

x = 2y + 7 (2)

Apply the substitution method :

Substitute the value of x from the equation (1) into the equation(2) and simplify for y

x = 2y + 7

7y + 18 = 2y + 7

7y - 2y = 7 -18

5y = -11

y = -11/5

Substitute this value in the equation (1)

x = 7y + 18

x = 7(-11/5) + 18

x = -77/5 + 18

x = 13/5

So, the solutions are y = -11/5 and x = 13/5

Answer : y = -11/5 and x = 13/5, (x,y) = (13/5, -11/5)

The graph of the equations are :

The lines intersect at a single point so, there are only one solution.