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4 years ago

Solve the system of equations below algebraically. 2x + 3y = 6 - 5x+2y=4

Mathematics

1 answer:

trapecia [35]4 years ago

4 0

Answer: The solution is (0,2)

Step-by-step explanation:

2x +3y = 6 We will solve the equations using the elimination method

-5x +2y= 4 but first we need to eliminate one of the variables and we will multiply the first equation by 5 and multiply the second equation by 2 to eliminate the x variable.

5(2x + 3y) =6(5) new equation : 10x +15y = 30

2(-5x + 2y) = 4(2) new equation ; -10x +4y =8

Now we have to new equations so we will eliminate the x term by adding

10x +15y = 30

-10x +4y =8

19y = 38 divide both sides by 19.

y= 2 Now using the solution for y plot it into one of the new equations and solve for x

10x + 15(2) = 30

10x + 30 = 30

-30 -30

10x = 0

x= 0

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3 years ago

Farmer Jones raises ducks and cows. He looks out his window and sees 54 animals with a total of 122 feet. If each animal is “nor

Olenka [21]

Answer:

He have 47 ducks and 7 cows.

Step-by-step explanation:

Given:

Farmer Jones raises ducks and cows.

He looks out his window and sees 54 animals with a total of 122 feet.

Now, to find the each type of animal he have.

Let the number of ducks be $x.$

And the number of cows be $y.$

So, total number of animals are:

$x+y=54$

$x=54-y$ ....( 1 )

As, the feet of cows are 4 and ducks are 2.

Now, the total number of feet are:

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$2x+4y=122$

Substituting the value of $x$ from equation (1) we get:

$2(54-y)+4y=122$

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$108+2y=122$

Subtracting both sides by 108 we get:

$2y=14$

Dividing both sides by 2 we get:

$y=7.$

The number of cows = 7.

Now, to get the number of ducks we substitute the value of $y$ in equation (1):

$x=54-y\\x=54-7\\x=47.$

The number of ducks = 47.

Therefore, he have 47 ducks and 7 cows.

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