$1$ . Hitung luas daerah yang dibatasi oleh perpotongan garis $x+y=4$ , garis $3 y-$ $2 x=2$ , serta sumbu $x$ pada rentang $0 \leq x \leq 3$ .

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1

. Hitung luas daerah yang dibatasi oleh perpotongan garis

x+y=4

, garis

3 y-

2 x=2

, serta sumbu

x

pada rentang

0 \leq x \leq 3

Rewrite equation for y: Rewrite the first equation to solve for y: $x + y = 4$ becomes $y = 4 - x$ .
Find point of intersection: Rewrite the second equation to solve for y: $3y - 2x = 2$ becomes $y = \frac{2 + 2x}{3}$ .
Solve for x: Find the point of intersection between the two lines by setting the y expressions equal to each other: $4 - x = \frac{2 + 2x}{3}$ .
Calculate y-coordinate: Multiply both sides by $3$ to clear the fraction: $3(4 - x) = 2 + 2x$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the $3x$ $1$ -coordinate of the intersection: $3x$ $2$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the $3x$ $1$ -coordinate of the intersection: $3x$ $2$ . Calculate $3x$ $1$ : $3x$ $4$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the $3x$ $1$ -coordinate of the intersection: $3x$ $2$ . Calculate $3x$ $1$ : $3x$ $4$ . Now we have the intersection point $3x$ $5$ . The area of the triangle formed by the $x$ -axis, the line $3x$ $7$ , and the line $3x$ $8$ is $3x$ $9$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the y-coordinate of the intersection: $3x$ $1$ . Calculate $3x$ $2$ : $3x$ $3$ . Now we have the intersection point $3x$ $4$ . The area of the triangle formed by the x-axis, the line $3x$ $5$ , and the line $3x$ $6$ is $3x$ $7$ . The base of the triangle is from $3x$ $8$ to $x = 2$ , so the base is $2$ units.
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the y-coordinate of the intersection: $3x$ $1$ . Calculate $3x$ $2$ : $3x$ $3$ . Now we have the intersection point $3x$ $4$ . The area of the triangle formed by the x-axis, the line $3x$ $5$ , and the line $3x$ $6$ is $3x$ $7$ . The base of the triangle is from $3x$ $8$ to $x = 2$ , so the base is $2$ units. The height of the triangle is the y-coordinate of the intersection point, which is $2$ units.
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the $3x$ $1$ -coordinate of the intersection: $3x$ $2$ . Calculate $3x$ $1$ : $3x$ $4$ . Now we have the intersection point $3x$ $5$ . The area of the triangle formed by the $x$ -axis, the line $3x$ $7$ , and the line $3x$ $8$ is $3x$ $9$ . The base of the triangle is from $2$ $0$ to $x = 2$ , so the base is $2$ units. The height of the triangle is the $3x$ $1$ -coordinate of the intersection point, which is $2$ units. Calculate the area: $2$ $5$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the y-coordinate of the intersection: $3x$ $1$ . Calculate $3x$ $2$ : $3x$ $3$ . Now we have the intersection point $3x$ $4$ . The area of the triangle formed by the x-axis, the line $3x$ $5$ , and the line $3x$ $6$ is $3x$ $7$ . The base of the triangle is from $3x$ $8$ to $x = 2$ , so the base is $2$ units. The height of the triangle is the y-coordinate of the intersection point, which is $2$ units. Calculate the area: Area = $2$ $2$ . Simplify the area calculation: Area = $2$ $3$ .
Calculate area: Distribute and simplify: $12 - 3x = 2 + 2x$ . Add $3x$ to both sides and subtract $2$ from both sides: $12 - 2 = 3x + 2x$ . Combine like terms: $10 = 5x$ . Divide both sides by $5$ to solve for $x$ : $x = 10 / 5$ . Calculate $x$ : $x = 2$ . Plug $x = 2$ into the first equation to find the y-coordinate of the intersection: $3x$ $1$ . Calculate $3x$ $2$ : $3x$ $3$ . Now we have the intersection point $3x$ $4$ . The area of the triangle formed by the x-axis, the line $3x$ $5$ , and the line $3x$ $6$ is $3x$ $7$ base $3x$ $8$ height. The base of the triangle is from $3x$ $9$ to $x = 2$ , so the base is $2$ units. The height of the triangle is the y-coordinate of the intersection point, which is $2$ units. Calculate the area: Area $2$ $3$ . Simplify the area calculation: Area $2$ $4$ . Finish the area calculation: Area $2$ $5$ .

111. Hitung luas daerah yang dibatasi oleh perpotongan garis x+y=4 x+y=4 x+y=4, garis 3y− 3 y- 3y− 2x=2 2 x=2 2x=2, serta sumbu x x x pada rentang 0≤x≤3 0 \leq x \leq 3 0≤x≤3.

$1$ . Hitung luas daerah yang dibatasi oleh perpotongan garis $x+y=4$ , garis $3 y-$ $2 x=2$ , serta sumbu $x$ pada rentang $0 \leq x \leq 3$ .