Question

If (x, y) is a solution to the system of equations, what is the value of x? 2x + 1/ 2 y = 2 1/ 2 x + 2y = 6

A)
4/17
B)
174
C)
4/15
D)
15/4

Answer 1

C) 4/15

Explanation:

The two equations ...

• 2x + 1/2y = 2
• 1/2x + 2y = 6

can be solved for x using Cramer's rule:

x = (2·2 -1/2·6)/(2·2 -1/2·1/2) = (4-3)/(4-1/4) = 1/(15/4)

x = 4/15

_____

Cramer's rule for the solution to ...

• ax +by = c
• dx +ey = f

is ...

• ∆ = ae-db
• x = (ce -fb)/∆
• y = (fa-dc)/∆