$\left\{\begin{array}{ccc}y=\frac{1}{2}x+5\\y=-\frac{3}{2}x-7\end{array}\right\\\\subtitute:\\\\\frac{1}{2}x+5=-\frac{3}{2}x-7\ \ \ \ |subtract\ 5\ from\ both\ sides\\\\\frac{1}{2}x=-\frac{3}{2}x-12\ \ \ \ |add\ \frac{3}{2}x\ to\ both\ sides\\\\\frac{4}{2}x=-12\\\\2x=-12\ \ \ \ |divide\ both\ sides\ by\ 2\\\boxed{x=-6}\\\\subtitute\ value\ of\ "x"\ to\ first\ equation:\\\\y=\frac{1}{2}\cdot(-6)+5=-3+5=\boxed2\\\\Answer:\boxed{\boxed{x=-6\ and\ y=2}}$

4 0

3 years ago

Joni has two cats in the yard, Stephen and Graham. If both animals gained 20 pounds, Stephen would be 25% heavier than Graham. F

tresset_1 [31]

Answer:

Stephen weighs 80 lbs

Graham weighs 60 lbs

Step-by-step explanation:

Let Stephen the cat = S

Let Graham the cat = G

25% heavier = 125% = 125/100 = 1.25

50% heavier = 150% = 150/100 = 1.5

If both animals gained 20 lbs, S would be 25% heavier than G:

S + 20 = 1.25(G + 20)

⇒ S = 1.25(G + 20) - 20

⇒ S = 1.25G + 5

If both animals lost 20 lbs, S would be 50% heavier than G:

S - 20 = 1.5(G - 20)

⇒ S = 1.5(G - 20) + 20

⇒ S = 1.5G - 10

Equate both equations for S, and solve for G:

S = S

⇒ 1.25G + 5 = 1.5G - 10

⇒ -0.25G = -15

⇒ G = 60

Substitute found value for G into one of the equations for S and solve for S:

S = 1.5G - 10

⇒ S = 1.5 x 60 - 10

⇒ S = 90 - 10

⇒ S = 80

Stephen weighs 80 lbs

Graham weighs 60 lbs

6 0

3 years ago