What is the solution to the system of equations below? HELP!!!! y = negative one-fourth x + 2 and 3 y = negative three-fourths x
minus 6 no solution infinitely many solutions (–16, 6) (–16, –2)
2 answers:
Answer:
No solution
Step-by-step explanation:
Step 1: Write out equations
y = -1/4x + 2
3y = -3/4x - 6
Step 2: Substitution
3(-1/4x + 2) = -3/4x - 6
Step 3: Distribute
-3/4x + 6 = -3/4x - 6
From here, we can see that we have the same slope but different y-intercept. This means that the 2 lines are parallel and therefore never intersect.
Alternatively, you could graph the equations and see that the 2 lines are parallel and never intersect.
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the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1
<h3>How to determine the equation</h3>
From the figure given, we can deduce the coordinates of the sides
For A
A ( 4,2)
For B
B ( 4, 5)
C ( 1, 2)
D ( 2, -4 )
E ( 5, -4)
F ( 2, -1)
The slope for BC
Slope =
Substitute the values for both B and C coordinates, we have
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Find the difference for both the numerator and denominator
Slope =
Slope = 1
We have the rotation for both point ( 0, 1)
y - y1 = m ( x - x1)
The values for y1 and x1 are 1 and 0 respectively and the slope m is 1
Substitute the values
y - 1 = 1 ( x - 0)
y - 1 = x
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y = x + 1
Thus, the equation in the slope-intercept of the side of triangle ABC that is perpendicular to segment EF is y = x + 1
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