Question

Use substitution to solve the system of equations. How many solutions are there? 12 x − 13 y = 5 x = 23 y + 10 There are no solutions. There is one solution. There are infinitely many solutions.

Answer 1

Answer: there is one solution

Explanation:

12x − 13y = 5

x = 23y + 10

lets substitute x into the first equation.

12(23y + 10) - 13y = 5

276y + 120 - 13y = 5

263y = -115

y = -115/263

substituting for x:

x = 23(-115/263) + 10

x = -2645/263 + 10

x = -15/263

As we can see, we get one value of x;

this means there is one solution