How do you solve #x + y = -7# and #3x + y = -9#?
You could solve this system of equations by using the multiplication method.
The system of equations will now be
This is equivalent to
The two solutions are
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To solve the system of equations: x + y = -7 3x + y = -9
You can use either the substitution method or the elimination method. Let's use the elimination method.
- Multiply one or both equations by appropriate constants to make the coefficients of one of the variables the same or additive inverses.
- Add or subtract the equations to eliminate one of the variables.
- Solve for the remaining variable.
- Substitute the value of the remaining variable into one of the original equations to find the value of the other variable.
- Check your solution by substituting the values of x and y into both original equations to ensure they satisfy both equations.
Using the elimination method:
Multiply the first equation by 3 to make the coefficient of y the same as in the second equation:
3(x + y) = 3(-7) 3x + 3y = -21
Now, subtract the second equation from this modified first equation:
(3x + 3y) - (3x + y) = -21 - (-9) 3x + 3y - 3x - y = -21 + 9 2y = -12
Now, solve for y:
2y = -12 y = -6
Substitute the value of y into one of the original equations to find x. Let's use the first equation:
x + (-6) = -7 x - 6 = -7 x = -7 + 6 x = -1
Therefore, the solution to the system of equations is x = -1 and y = -6.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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