A system of equations has infinitely many solutions when the two equations are dependent, meaning one equation is a multiple of the other. In this case, we can see that the second equation is equal to -5 times the first equation.
To confirm this, let's multiply the first equation by -5:
-5(-x - y) = -5(35)
5x + 5y = -175
We can see that the second equation is exactly the same as 5x + 5y = -175.
Since the two equations are equivalent, any values of x and y that satisfy one equation will automatically satisfy the other equation.
For example, let's choose x = 1. Plugging this into the first equation:
-1 - y = 3
y = -4
Now let's plug these values into the second equation:
1 + 5(-4) = -15
-19 = -15
The values x = 1 and y = -4 satisfy both equations. If we choose any other values for x and y that satisfy one equation, they will also satisfy the other equation. Therefore, the system of equations has infinitely many solutions.
The following system of equations has infinitely many solutions. Explain what it means for a system of equations to have infinitely many solutions. Use calculations and/or examples to justify your answer. {−x−y=35x+5y=−15
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