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## Answers

**Eliminate y:**

**- kx + y = 3 ⇒ Equation 1**

**4x - y = 2 ⇒ Equation 2**

**-kx : 4x = 3 : 2**

**-kx (2) = 4x (3)**

**-2xk = 12x**

**-2xk/-2x = 12x/-2x**

__k = - 6__**Solve the system, substitute - 6 for k in Equation 1**

**-(-6)x + y = 3**

**6x + y = 3**

**y = -6x + 3 ⇒ Equation 3**

**Substitute for x by - 6x + 3 for y in Equation 2:**

**4x - (-6x + 3) = 2**

**4x + 6x - 3 = 2**

**10x = 2 + 5**

**10x/10 = 5/10**

**x = 1/2**

**Solve for y, by substituting 1/2 to x in Equation 3:**

**y = -6x + 3**

**y = -6(1/2) + 3**

**y = - 3 + 3**

**y = 0**

**The solution to the system is (1/2, 0).**

**To check, x = 1/2; y = 0**

**Equation 1:**

**6x + y = 3**

**6 (1/2) + 0 = 3**

**3 + 0 = 3**

**3 = 3**

**Equation 2:**

**4x - y = 2**

**4 (1/2) - 0 = 2**

**2 - 0 = 2**

**2 = 2**

**Therefore**

**- 6****for**

**k****satisfies the system as consistent and independent with only one solution (1/2, 0) which is the point of intersection of the given two equations/graphs.**