# y = 3.5x – 3.5 y = -3.5x + 3.5: How many solutions will this system of equations have?

A: No solution

B: Infinite solutions

C: One solution

D: Two solutions

• y = 3.5x – 3.5

y = -3.5x + 3.5

7.5x = 7.5

x = 1, y = 0

C: One solution

• 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.

• 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 !!