# Solving by Elimination and Dependent and Inconsistant Systems

1. Solving a system by elimination. Solve each system of equations:

a. 2x - y + 3z = 14

b. X + y = 2z = -5

c. 3x + y - z = 2

d. x - 3y + 2z = -11

e. 2x + 4y + 3z = -15

f. 3x - 5y - 4z = 5

2. Dependent and Inconsitent systems. Solve each system:

a. 4x - 2y - 2z = 5

b. 2x - y - z = 7

c. -4x + 2y + 2z = 6

3. Paranoia. Fearful of a bank failure. Norman split his life savings of $600,000 among three banks. He received 5%, 6% and 7% on the three deposits. In the account earning 7% interest he deposited twice as much as in the account earning 5% interest. If his total earnings were $3760 then how much did he deposit in each account?

4. Pocket change. Harry has $2.25 in nickels, dimes and quarters. If he had twice as many nickels, half as many dimes and the same number of quarters, he would have $2.50. If he has 27 coins altogether then how many of each does he have?

5. Three digit number. The sum of the digits of a three digit number is 11. If the digits are reversed, the new number is 46 more than five times the old number. If the hundreds digit pus twice the ten digit is equal to the units digit then what is the number?

6. Finding the vertex, focus and directixy. Find the vertex, focus and directrix:

Y = 1/2x^2

7. Find the equation of the parabola with the given focus and directrix:

Focus (-4,5) directrix y = 4

8. Changing forms. Write the equation in the form y = a(x - h)^2 + k

Identify the vertex, focus, directrix and axis of symmetry of the parabola:

Y = -3x^2-6 + 7

9. Find the vertex, focus, directrix and axis of symmetry of the parabola (Without completeing the square) and determine whether the parabola opens upward or downward.

a. Y = 2x^2 + 4x - 3

b. Y = -2x^2 - 6

10. Graph both equations of each system on the same coordinate axes. Use elimination of variables to find all points of intersection:

a. Y = x^2 + 5x + 6

b. Y = x + 11.

#### Solution Preview

Section 4.3

#14 Solving a system by elimination. Solve each system of equations

2x-y+3z=14 (I)

X+y+2z=-5 (II)

3x+y-z=2 (III)

(I)+(II): 3x+5z=9 (IV)

(III)+(I): 5x+2z=16 (V)

(IV)*5-3*(V): 19z=45-48, z=-3/19

Plug z=-3/19 into (V), x=(16+6/19)/5=62/19

Plug into (II): y=-5-2*(-3)/19-62/19=-151/19

Therefore, the solution is x=62/19, y=-151/19, z=-3/19

#18 x-3y+2z= -11 (I)

2x+4y+3z= -15 (II)

3x-5y-4z=5 (III)

(II)-2*(I): 10y-z=7 (IV)

(III)-3*(I): 4y-10z=38 (V)

(IV)*2-5*(V): 48z=14-38*5, z=-11/3

Plug into (IV): y=(-11/3+7)/10=1/3

Plug y=1/3, z=-11/3 into (I): x=-11-2*(-11/3)+3*(1/3)=-8/3

Therefore, the solution is x=-8/3, y=1/3, z=-11/3.

#34 Dependent and Inconsitent systems. Solve each system

4x-2y-2z=5 (I)

2x-y-z=7 (II)

-4x+2y+2z=6 (III)

(I)-2*(II): 4x-2y-2z-2(2x-y-z)=5-7*2

0=-9.

Since 0 is not equal to -1, there is no solution for this system.

#48 Paranoia. Fearful of a bank failure. Norman split his life savings of $600,000 among three banks. He received 5%, 6% and 7% on the three deposits. In the account earning 7% interest he deposited twice as much ...

#### Solution Summary

The solution assists with solving by elimination and dependent and inconsistent systems.