Question1) Determine if the ordered pair $(3,4)$ is a solution to the equation $6 x-4 y=6$ . Find a point that does belong to this line.

Studdy Solution

STEP 1

1. The equation given is $6x - 4y = 6$ .
2. An ordered pair $(x, y)$ is a solution to the equation if substituting $x$ and $y$ into the equation makes it true.
3. To find a point on the line, we can choose a value for $x$ or $y$ and solve for the other variable.

STEP 2

1. Substitute the ordered pair $(3, 4)$ into the equation and verify if it satisfies the equation.
2. Find a point that lies on the line by choosing a value for $x$ or $y$ and solving for the other variable.

STEP 3

Substitute $x = 3$ and $y = 4$ into the equation $6x - 4y = 6$ :
$6(3) - 4(4) = 6$
Calculate the left side:
$18 - 16 = 2$
Since $2 \neq 6$ , the ordered pair $(3, 4)$ is not a solution to the equation.

STEP 4

To find a point on the line, let's choose $x = 0$ and solve for $y$ :
Substitute $x = 0$ into the equation:
$6(0) - 4y = 6$
This simplifies to:
$-4y = 6$
Solve for $y$ by dividing both sides by $-4$ :
$y = -\frac{6}{4} = -\frac{3}{2}$
Thus, the point $(0, -\frac{3}{2})$ is on the line.
The ordered pair $(3, 4)$ is not a solution, but the point $(0, -\frac{3}{2})$ lies on the line.

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