The solution to given system of equations is [tex](x, y) = (\frac{-15}{263} , \frac{-115}{263})[/tex]
The given equation has one solution
Solution:
Given system of equations are:
12x - 13y = 5 --------- eqn 1
x = 23y + 10 --------- eqn 2
We have to solve the system of equations by substitution
Substitute eqn 2 in eqn 1
12(23y + 10) - 13y = 5
276y + 120 - 13y = 5
263y = 5 - 120
263y = -115
[tex]y = \frac{-115}{263}[/tex]
Substitute the above value of "y" in eqn 2
[tex]x = 23 \times \frac{-115}{263} + 10\\\\x = \frac{-2645}{263} + 10\\\\x = \frac{-2645 + 2630}{263}\\\\x = \frac{-15}{263}[/tex]
Thus the solution to given system of equations is [tex](x, y) = (\frac{-15}{263} , \frac{-115}{263})[/tex]
Thus the given equation has one solution
