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3 years ago

Solve the system of equations by graphing: 2x + 3y = 2 6x + 18y = 9

Mathematics

1 answer:

cluponka [151]3 years ago

7 0

The answer is A: x=1/2 , y= 1/3

Solve the following system:
{2 x + 3 y = 2 | (equation 1)
{6 x + 18 y = 9 | (equation 2)

Swap equation 1 with equation 2:
{6 x + 18 y = 9 | (equation 1)
{2 x + 3 y = 2 | (equation 2)

Subtract 1/3 × (equation 1) from equation 2:
{6 x + 18 y = 9 | (equation 1)
{0 x - 3 y = -1 | (equation 2)

Divide equation 1 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x - 3 y = -1 | (equation 2)

Multiply equation 2 by -1:
{2 x + 6 y = 3 | (equation 1)
{0 x+3 y = 1 | (equation 2)

Divide equation 2 by 3:
{2 x + 6 y = 3 | (equation 1)
{0 x+y = 1/3 | (equation 2)

Subtract 6 × (equation 2) from equation 1:
{2 x+0 y = 1 | (equation 1)
v0 x+y = 1/3 | (equation 2)

Divide equation 1 by 2:
{x+0 y = 1/2 | (equation 1)
v0 x+y = 1/3 | (equation 2)

Collect results:
Answer: {x = 1/2, y = 1/3

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Can somebody please help me with this problem please

Furkat [3]

Answer:

m = 3, n = 4

Step-by-step explanation:

Solve using the substitution process. First, start with the second equation:

2m + 2n = 14

Simplify. Divide 2 from all terms within the equation. What you do to one side, you do to the other:

(2m + 2n)/2 = (14)/2

m + n = 7

Isolate the variable m. Subtract n from both sides:

m + n (-n) = 7 (-n)

m = 7 - n

Plug in 7 - n for m in the first equation:

-5m + 9n = 21

-5(7 - n) + 9n = 21

Solve. First, distribute -5 to all terms within the parenthesis:

(-35 + 5n) + 9n = 21

Simplify. Combine like terms:

-35 + (5n + 9n) = 21

-35 + 14n = 21

Isolate the variable, n. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS. First, add 35 to both sides:

14n - 35 (+35) = 21 (+35)

14n = 21 + 35

14n = 56

Isolate the variable n. Divide 14 from both sides:

(14n)/14 = (56)/14

n = 56/14

n = 4

Plug in 4 to n in one of the equations, and solve for m.

2m + 2n = 14

2m + 2(4) = 14

2m + 8 = 14

Isolate the variable, m. Do the opposite of PEMDAS. First, subtract 8 from both sides:

2m + 8 (-8) = 14 (-8)

2m = 14 - 8

2m = 6

Divide 2 from both sides:

(2m)/2 = (6)/2

m = 6/2

m = 3

Your answers: m = 3, n = 4

6 0

3 years ago

Read 2 more answers

The following three shapes are based only on squares, semicircles, and quarter circles. Find the perimeter and the area of each

MakcuM [25]

The perimeter = 4 * length of a semicircle of radius 5 == 4* pi * 5 = 20 pi cm

The area of one of the clear parts = 1/2 area of square - area semicircle

= 1/2 * 10^2 - 1/2 pi *5^2 = 50 - 12.5pi

So area of shaded parts = area of square - 4 (50 - 12.5pi)
= 100 - 200 + 100pi = (100pi - 100) cm^2

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kvv77 [185]

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