Question
use substitution method to solve system
{4x-3y=-5}
{8x-6y=-10}
{4x-3y=-5}
{8x-6y=-10}
Answers
GPT 3.5
To solve the system using the substitution method, we need to solve one equation for either x or y and substitute it into the other equation.
First, let's solve the first equation for x:
4x - 3y = -5
4x = 3y - 5
x = (3y - 5) / 4
Now, substitute this expression for x into the second equation:
8x - 6y = -10
8((3y - 5) / 4) - 6y = -10
2(3y - 5) - 6y = -10
6y - 10 - 6y = -10
-10 = -10
Since -10 = -10 is a true statement, this means that the system is dependent and the two equations represent the same line. Thus, there are infinitely many solutions to the system.
First, let's solve the first equation for x:
4x - 3y = -5
4x = 3y - 5
x = (3y - 5) / 4
Now, substitute this expression for x into the second equation:
8x - 6y = -10
8((3y - 5) / 4) - 6y = -10
2(3y - 5) - 6y = -10
6y - 10 - 6y = -10
-10 = -10
Since -10 = -10 is a true statement, this means that the system is dependent and the two equations represent the same line. Thus, there are infinitely many solutions to the system.