2x=3y-1 6x-9y=-3 How many solutions does the system have? Exactly one Solution No Solution Infinite Solution If it is exactly one solution, what is this solution?
Mathematics · College · Tue Nov 03 2020
Answered on
Given:
2x = 3y -1
6x - 9y = -3
Determine the number of solutions that the system have.
Solution:
In order to determine the number of solutions that the system of equations have, we equate the two equations into one solution.
3y -2x - 1 = 6x - 9y - 3
Transpose 6x - 9y -3 on the other side of the equation, hence we must take note that when transposing a number, the sign changes. After transposing we combine the similar terms.
= 3y -2x - 1 - 6x + 9y + 3
=12y - 8x + 4
Factor out 4 on the equation.
= 4(3y - 2x + 1)
Solve for y.
3y = 2x + 1
y = ⅔x + ⅓
Substitute y on the equation.
= 3(⅔x + 1) - 2x+ 1
= 2x + 3 - 2x + 1
= 3
Final answer:
= 3