Question

Help please must show work 5, 6, 7, 8 ,9

Answer 1

(5)

2r + s = 11 → (1)

r - s = 2 → (2)

add (1) and (2) term by term

3r = 13 ⇒ r = $\frac{13}{3}$

substitute this value into (2)

- s = $\frac{6}{3}$ - $\frac{13}{3}$ = - $\frac{7}{3}$

hence s = $\frac{7}{3}$

(6)

substitute y = 3 - x into the other equation

5x + 3(3 - x) = - 1

5x + 9 - 3x = - 1

2x + 9 = - 1 ( subtract 9 from both sides )

2x = - 10 ( divide both sides by 2 )

x = - 5

substitute x = - 5 into y = 3 - x

y = 3 - (- 5) = 3 + 5 = 8

(7)

add both equations to eliminate the term in b

22a = 0 ⇒ a = 0 and b = 0

(8)

Since both equations express y in terms of x , equate the right sides

3x - 1 = 2x - 5 ( subtract 2x from both sides )

x - 1 = - 5 ( add 1 to both sides )

x = - 4

substitute this value into either of the 2 equations

y = - 8 - 5 = - 13

(9)

2y = 8 - 7x → (1)

4y = 16 - 14x → (2)

multiply (1) by 2

4y = 16 - 14x

Both equations are equal hence any value of x will make them true

example (1, $\frac{1}{2}$) is a possible solution

The system has an infinite number of solutions