Question
\[ \begin{array}{r}y=-6 x-7 \\ y=-7 x\end{array} \] Answer Attempt out of 2
Ask by Bright Hamilton. in the United States
Feb 25,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The lines intersect at the point (7, -49).
Solution
To find the point where the two lines intersect, set the right-hand sides of the equations equal to each other since both equal y.
Step 1: Write the equations:
y = -6x - 7
y = -7x
Step 2: Set them equal:
-6x - 7 = -7x
Step 3: Solve for x:
Add 7x to both sides:
7x - 6x - 7 = 0
x - 7 = 0
So, x = 7
Step 4: Substitute x back into one of the original equations (using y = -7x):
y = -7(7) = -49
Thus, the point of intersection is (7, -49).
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Simplify this solution Mind Expander
To find the intersection point of the two lines defined by the equations \( y = -6x - 7 \) and \( y = -7x \), set them equal to each other: \[ -6x - 7 = -7x \] Rearranging gives: \[ -x - 7 = 0 \] So, \[ x = -7 \] Now, plug \( x = -7 \) back into either equation to find \( y \). Using \( y = -7x \): \[ y = -7(-7) = 49 \] Thus, the intersection point is \((-7, 49)\). Also, remember that accurately solving and graphing linear equations can visually depict relationships and intersections. Using graphing tools (like a graphing calculator or software) can give insights into the behavior of multiple linear functions, which can be super handy for visual learners!
