The solution to a system of equations represents the point where the two equations intersect. Thus, the solution to the system of equations consisting of linear equation A and linear equation B is the point that is common to both equations.
We can determine the equation for line A using the two given points: (-7,4) and (3,-10). Using the formula for the equation of a line (y = mx + b), we can find the slope of line A:
m = (y2 - y1) / (x2 - x1)
m = (-10 - 4) / (3 - (-7))
m = -14 / 10
m = -7/5
Using the slope-intercept form of a line, we can find the y-intercept (b) of line A:
y = mx + b
4 = (-7/5)(-7) + b
4 = 49/5 + b
4 - 49/5 = b
20/5 - 49/5 = b
-29/5 = b
So, the equation for line A is y = (-7/5)x - 29/5.
Using the same process, we can find the equation for line B using the points (-7,4) and (5,11):
m = (11 - 4) / (5 - (-7))
m = 7/12
y = (7/12)x + b
4 = (7/12)(-7) + b
b = 4 + 49/12
b = 48/12 + 49/12
b = 97/12
Therefore, the equation for line B is y = (7/12)x + 97/12.
To find the point of intersection, we can set the two equations equal to each other and solve for x:
(-7/5)x - 29/5 = (7/12)x + 97/12
Multiplying both sides of the equation by 60 to eliminate the fractions:
-12(7)x - 12(29) = 5(7)x + 5(97)
-84x - 348 = 35x + 485
-119x = 833
x = -833/119
Substituting this value back into one of the equations, we can find the corresponding y-value:
y = (-7/5)(-833/119) - 29/5
y = 5831/595
Therefore, the point of intersection is approximately (-833/119, 5831/595).
None of the given points (−7,4), (3,−10), (5,11), or (7,4) match this point. Therefore, the solution to the system of equations is not one of the given points.
The correct answer is none of the above.
The graph of linear equation A passes through the points (−7,4)
and (3,−10)
, while the graph of linear equation B passes through the points (−7,4)
and (5,11)
. Which of these is a solution to the system of equations consisting of linear equation A and linear equation B?
A
(−7,4)
B
(3,−10)
C
(5,11)
D
(7,4)
1 answer