y = 3.5x – 3.5 y = -3.5x + 3.5: How many solutions will this system of equations have?
Consider the following system of equations:
- ( y = 3.5x - 3.5 )
- ( y = -3.5x + 3.5 )
How many solutions does this system of equations have?
A: No solution
B: Infinite solutions
C: One solution
D: Two solutions
5 Answers
Dec 03, 2024
Since the variables has a power of 1 that is it will have only one solution. ANS: C
Given: Y = 3.5x – 3.5 y = -3.5x + 3.5 or
y = 3.5(x-y)..:eq(1)
y = 3.5(1-x)…:eq(2)
From eq(1): 3.5x = (3.5+1)y = 4.5y or
x = (4.5/3.5)y = (9/7)y = 1.286y and
Substitute the value of x in eq(2):
y = 3.5(1-1.286y) or
2.286y = 3.5 => y = 3.5/2.286 = 1.531
substitute value of y in eq(1):
x = 1.286y = 1.286 * 1.531 = 1.969
Verification:
y = 3.5(x-y) = 3.5(1.969-1.531) = 3.5 * 0.438 = 1.532
C: one solution
Graphed on the plane, these are two lines. They are not parallel, and they are not the same line. They have different slopes.
So they will intersect, and if two lines intersect in a plane, they will only intersect once.
Jan 09, 2025
Well,
we have :
y = 3.5x – 3.5
y = -3.5x + 3.5
these are two lines with different slopes : -3.5 and 3.5
therefore:
they intersect !!
C: One solution <—- ANSWER
hope it’ ll help !!
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