Use substitution to solve the system. Use Example 9 as a guide. y = 1/6 x -7 and y= 1/7 x -6

Question

Use substitution to solve the system. Use Example 9 as a guide.

y = 1/6 x -7 and y= 1/7 x -6

The numbers are fractions.

Answer 1

y=1/6x - 7

y = 1/7x -6

1/6x -7 = 1/7x =6

1/6x - 1/7x = 7-6 = 1

(7-6)/42x

x = 1/42

substitute that into either original equation, y=0

(x,y) = (1/42, 0) x= 1/42, y = 0

UNLESS you really meant y=(1/6)x-7 and y=(1/7)x-6

THEN y=0, x=42 or (x,y) = (42,0)

Odds are you meant the latter, nicer solution, no fractions.

You could also work this with linear or matrix algebra

1/6 -1 7

1/7 -1 6

reduced to

1 -6 42

1 -7 42 reduced to

1 -6 42

0 1 0 and

1 0 42

0 1 0

x=42, y=0 1st column is x, 2nd is y, 3rd column is the solution

(this would probably make more sense, if there wasn't ("were not" for English teachers of the the correct verb) a pandemic with major stress, and a gasoline shortage with people waiting in gas lines for hours, in Atlanta if they can find an open gas station, and up to $9 per gallon in some places. Add in a little political divisiveness & possible new war in the Middle East, and major migration on our Southern border. But ignore that. Math is pure logic, no arguments, if you get it right, and even if you don't you get partial credit for partial right. IF you get it right and people disagree, you win in the end, regardless. Just give it time. Half the problem though is figuring out what the problem really is. Mistakes are endemic, a plague, a pandemic, not easily "flattened" or reduced to herd immunity & there's no vaccine, Yet.)