One of the equations of a system is" x + 3y = -5. Which equation, when combined with the given equation, would create a system that had a unique solution?*1 pointx - 3y= -5x + 3y = -102x + 6y = -53x + 9y = -15
Question
One of the equations of a system is" x + 3y = -5. Which equation, when combined with the given equation, would create a system that had a unique solution?*1 pointx - 3y= -5x + 3y = -102x + 6y = -53x + 9y = -15
Solution
To find a unique solution for a system of linear equations, the two equations must not be multiples of each other. This means their slopes must be different.
The slope of the given equation, x + 3y = -5, can be found by rearranging it into slope-intercept form (y = mx + b), where m is the slope.
Rearranging, we get: 3y = -x - 5 y = -1/3x - 5/3
So, the slope of the given equation is -1/3.
Now, let's find the slopes of the other equations:
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x - 3y = -5 Rearranging, we get: 3y = x + 5 y = 1/3x + 5/3 The slope is 1/3. This equation has a different slope from the given equation, so it would create a system with a unique solution.
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x + 3y = -10 Rearranging, we get: 3y = -x - 10 y = -1/3x - 10/3 The slope is -1/3. This equation has the same slope as the given equation, so it would not create a system with a unique solution.
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