Question 1 Solve the system of equation by the substitution method. o a (12, 6))

Question

Question 1 Solve the system of equation by the substitution method. o a (12, 6)) o (12, -61) Question2 Ewa lwate the piecewise function at the given walve of the independent wariabie Sx + Find f(-3). O C-12 o D. 17 and -12 Question3 Use properties of logarithms to expand the logarithmic expression as much as possible Where possible, ewalute logarithmic expressions without using a ca ículator () 2.11 o A loge8 o B. 109s22 loge5 o D. 10gs 2+109s 11 1096 5 Question 4 Perform the multiplication and write the expression showm below in standard form. 4-30-3-50 o 8.3-29i OD-27-29i

Explanation / Answer

1.We have x+y = -4 …(1) and y = -3x…(2). On substituting y = -3x in the 1st equation, we get x-3x = -4 or, -2x = -4 so that x = -4/-2 = 2. Then y = -3*2 = -6. The answer is x = 2, y = -6.

2. We have f(x) = 5x+3 if x < -3 and f(x) = -4x+5 if x -3. Hence f(-3) = -4*(-3)+5 = 12+5 = 17.Option B is the correct answer.

3. We know that loga(mn) = loga(m) + loga(n) and loga(m/n) = loga(m) – loga(n) . +log611. Hence log6(2*11/5) = log6(2*11)-log6 5 = log6 2 +log6 11- log6 5 . Option (d) is the correct answer.

4. (4-3i)(-3-5i) = -12-20i+9i+15i2 = -12-11i -15 (as i2= -1) = -27-11i. Option A is the correct answer.

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