QuestionFind the values of $x$ and $y$ that satisfy the equation $2x + 3y = 12$ for the point $(3,1)$ .

Studdy Solution

STEP 1

Assumptions1. We have a point $(3,1)$ . We have a linear equation $x+3y=12$
3. We need to check if the given point lies on the line represented by the equation.

STEP 2

The general form of a linear equation is $ax+by=c$ . If a point $(x0, y0)$ satisfies this equation, then the point lies on the line.
So, we need to substitute $x=$ and $y=1$ into the equation $2x+y=12$ and check if both sides of the equation are equal.

STEP 3

Substitute $x=3$ and $y=1$ into the equation.
$2(3) +3(1) =12$

STEP 4

Calculate the left side of the equation.
$2(3) +3(1) =6 +3 =9$

STEP 5

Compare the calculated left side of the equation with the right side.Since $9 \neq12$ , the point $(3,1)$ does not lie on the line $2x+3y=12$ .

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QuestionFind the values of $x$ and $y$ that satisfy the equation $2x + 3y = 12$ for the point $(3,1)$ .

Studdy Solution

STEP 1

Assumptions1. We have a point $(3,1)$ . We have a linear equation $x+3y=12$
3. We need to check if the given point lies on the line represented by the equation.

STEP 2

The general form of a linear equation is $ax+by=c$ . If a point $(x0, y0)$ satisfies this equation, then the point lies on the line.
So, we need to substitute $x=$ and $y=1$ into the equation $2x+y=12$ and check if both sides of the equation are equal.

STEP 3

Substitute $x=3$ and $y=1$ into the equation.
$2(3) +3(1) =12$

STEP 4

Calculate the left side of the equation.
$2(3) +3(1) =6 +3 =9$

STEP 5

Compare the calculated left side of the equation with the right side.Since $9 \neq12$ , the point $(3,1)$ does not lie on the line $2x+3y=12$ .

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QuestionFind the values of xxx and yyy that satisfy the equation 2x+3y=122x + 3y = 122x+3y=12 for the point (3,1)(3,1)(3,1).

Studdy Solution

STEP 1

Assumptions1. We have a point (3,1)(3,1)(3,1). We have a linear equation x+3y=12x+3y=12x+3y=123. We need to check if the given point lies on the line represented by the equation.

STEP 2

The general form of a linear equation is ax+by=cax+by=cax+by=c. If a point (x0,y0)(x0, y0)(x0,y0) satisfies this equation, then the point lies on the line.So, we need to substitute x=x=x= and y=1y=1y=1 into the equation 2x+y=122x+y=122x+y=12 and check if both sides of the equation are equal.

STEP 3

Substitute x=3x=3x=3 and y=1y=1y=1 into the equation.2(3)+3(1)=122(3) +3(1) =122(3)+3(1)=12

STEP 4

Calculate the left side of the equation.2(3)+3(1)=6+3=92(3) +3(1) =6 +3 =92(3)+3(1)=6+3=9

STEP 5

Compare the calculated left side of the equation with the right side.Since 9≠129 \neq129=12, the point (3,1)(3,1)(3,1) does not lie on the line 2x+3y=122x+3y=122x+3y=12.

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QuestionFind the values of $x$ and $y$ that satisfy the equation $2x + 3y = 12$ for the point $(3,1)$ .

Assumptions1. We have a point $(3,1)$ . We have a linear equation $x+3y=12$
3. We need to check if the given point lies on the line represented by the equation.

The general form of a linear equation is $ax+by=c$ . If a point $(x0, y0)$ satisfies this equation, then the point lies on the line.
So, we need to substitute $x=$ and $y=1$ into the equation $2x+y=12$ and check if both sides of the equation are equal.

Substitute $x=3$ and $y=1$ into the equation.
$2(3) +3(1) =12$

Calculate the left side of the equation.
$2(3) +3(1) =6 +3 =9$

Compare the calculated left side of the equation with the right side.Since $9 \neq12$ , the point $(3,1)$ does not lie on the line $2x+3y=12$ .