−6x+2y=−26 ; 8x−8y=24

Mathematics

1 answer:

Eva8 [605]3 years ago

8 0

The solution is: x=5, y=2

Step-by-step explanation:

Given equations are:

$-6x+2y=-26\ \ \ \ \ Eqn\ 1\\8x-8y=24\ \ \ \ \ \ \ Eqn\ 2\\Multiplying\ equation\ 1\ by\ 4\\4(-6x+2y)=4(-26)\\-24x+8y=-104\ \ \ Eqn\ 3\\Adding\ Eqn\ 2\ and\ Eqn\ 3\\-24x+8y+8x-8y=24-104\\-16x=-80\\dividing\ both\ sides\ by\ -16\\\frac{-16x}{-16}=\frac{-80}{-16}\\x=5\\Putting\ x=5\ in\ equation\ 1\\-6(5)+2y=-26\\-30+2y=-26\\Adding\ 30\ on\ both\ sides\\-30+2y+30=-26+30\\2y=4\\Dividing\ both\ sides\ by\ 2\\\frac{2y}{2}=\frac{4}{2}\\y=2$

Verification:

$8x-8y=24\\Putting\ x=5\ and\ y=2\\8(5)-8(2)=24\\40-16=24\\24=24$

The solution is: x=5, y=2

Keywords: Linear Equations, Elimination method

Learn more about linear equations at:

#LearnwithBrainly

You might be interested in

PLEASE HELP MEEEEE!!!!!!!

OverLord2011 [107]

Answer:

Cheese: $4\frac{3}{8}$
Milk: $1\frac{2}{3}$
Pasta: $6\frac{1}{4}$

Step-by-step explanation:

Cheese:

$1\frac{3}{4} = \frac{7}{4}$
Set up a proportion: $\frac{\frac{7}{4} }{4} = \frac{x}{10}$
Cross multiply, then divide: 10 × 7/4 = 17.5, 17.5 ÷ 4 = 4.375
$4.375 = 4\frac{3}{8}$

Milk:

Set up a proportion: $\frac{\frac{2}{3} }{4} = \frac{x}{10}$
Cross multiply, then divide: 10 × 2/3 = $6\frac{2}{3}$ , $6\frac{2}{3}$ ÷ 4 = $1\frac{2}{3}$