Solve for x and y: 7x + 3y = 42 4x + 6y = 36
A)x = -4.8, y = 2.8
B)x = 4.8, y = 2.8
C)x = -4.8, y = -2.8
D)x = 4.8, y = -2.8
E)x = 4.8, y = -5.6

Question

Quizplus · Accepted Answer

First, we can rearrange the equations to be in slope-intercept form (y = mx + b):
7x + 3y = 42  ->  3y = -7x + 42  ->  y = (-7/3)x + 14
4x + 6y = 36  ->  6y = -4x + 36  ->  y = (-4/6)x + 6
Then, we can see that the slopes of the two lines are different (-7/3 and -4/6), so they will intersect at a single point. We can solve for x by setting the two equations equal to each other:
(-7/3)x + 14 = (-4/6)x + 6
Multiplying both sides by 6 to clear the fractions:
-14x + 84 = -4x + 36
Combining like terms:
-10x = -48
x = 4.8
Substituting x back into either equation to solve for y:
y = (-7/3)(4.8) + 14 = 2.8
Therefore, the solution is x = 4.8 and y = 2.8, which corresponds to answer choice B.

Solve for X and Y: 7x + 3y = 42