The system of equations is dependent, yielding infinitely many solutions in the form (t, -2t - 10), where t is any real number.
To find the values of x and y that satisfy the given system of equations, follow these steps:
Start with the first equation: 2x + y = -10.
Rewrite the second equation by isolating y: -y = 2x + 10. Multiply both sides by -1 to make it easier to work with: y = -2x - 10.
Now that we have an expression for y in terms of x, substitute this expression into the first equation:
2x + (-2x - 10) = -10.
Simplify the equation:
2x - 2x - 10 = -10,
which simplifies to -10 = -10.
The equation -10 = -10 is always true, indicating that the system of equations is dependent and has infinitely many solutions.
Express the solution in terms of a parameter. Let's use t as a parameter:
x = t,
y = -2t - 10.
So, the system has infinitely many solutions in the form (t, -2t - 10), where t can be any real number.
Complete question:
What are the values of x and y that satisfy the system of equations:
2x + y = -10
-y = 2x + 10