Solve the system of linear equations by elimination. x+4y=6 −x−2y=−4

Mathematics

1 answer:

REY [17]3 years ago

3 0

Answer:

(x , y) = (2 , 1)

Step-by-step explanation:

// Solve equation [1] for the variable x

[1] x = -4y + 6

// Plug this in for variable x in equation [2]

[2] -(-4y+6) - 2y = -4

[2] 2y = 2

// Solve equation [2] for the variable y

[2] 2y = 2

[2] y = 1

// By now we know this much :

x = -4y+6

y = 1

// Use the y value to solve for x

x = -4(1)+6 = 2

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2 years ago

Dude is making 12 pounds of nut mixture with macadamia nuts and almonds. Macadamia nuts cost $9 per pound and almonds cost $5.25

pshichka [43]

Number of pounds of macadamia nuts is 8 pounds and number of pounds of almonds is 4 pounds.

<u>Step-by-step explanation:</u>

Step 1:

Given total pounds of mixture = 12 pounds, cost of macadamia nuts per pound = $9, cost of almonds per pound = $5.25, total cost of mixture per pound = $7.75.

Let number of pounds of macadamia nuts be x and number of pounds of almonds be 12-x.

Step 2:

Form an equation using the above information.

⇒ 9x + 5.25 (12-x) = 12 × 7.75

⇒ 9x + 63 - 5.25x = 93

⇒ 9x - 5.25x = 30

⇒ 3.75x = 30

⇒ x = 8

Number of macadamia nuts is 8 pounds.

Step 3:

Calculate number pounds of almonds

⇒ Number of pounds of almonds = 12 - x = 4 pounds.