SOLUTION: Solve the following system of equations.
5 x - 4 y = 1
-10 x + 8 y = -2
Please write your solution(s) in the ordered-pair form.
If there is no solution, please type "No
Question 1178178: Solve the following system of equations.
5 x - 4 y = 1
-10 x + 8 y = -2
Please write your solution(s) in the ordered-pair form.
If there is no solution, please type "None".
If there are infinitely many solutions, then type "Infinitely Many Solutions". Answer by ikleyn(52754) (Show Source):
Consider the extended matrix.
It is easy to see that its rows are proportional.
The proportionality coefficient is -2.
It means that one equation is equivalent to the other equation,
so FACTUALLY you have only one equation in two unknowns.
Such system has INFINITELY MANY solutions.
Take x as a FREE variable and express y = from the first equation.
You may give any value to x and calculate the respective value of y: each such a pair (x,y) will be a solution.
