Solve the following system of linear equations by substitution and determine whether the system has one solution, no solution or an infinite number of solutions. 2x+2y=-10 x+y=-5 selecting an option will enable input for any required text boxes. If the selected option does not have any associated text boxes then no further input is required
To solve the system of linear equations by substitution, we'll solve one equation for one variable and substitute it into the other equation.
In this case, we'll solve the second equation for x:
x + y = -5
x = -5 - y
Now, substitute this expression for x into the first equation:
2x + 2y = -10
2(-5 - y) + 2y = -10
-10 - 2y + 2y = -10
-10 = -10
The equation simplifies to -10 = -10, which is always true.
Since this equation is always true, there are infinitely many solutions to the system of linear equations.
Therefore, the system has an infinite number of solutions.