Solved on Jan 17, 2024

Is the point ( $7, 10$ ) a solution to the equation $y = 8x - 7$ ?

STEP 1

Assumptions
1. The given point is $(7,10)$ .
2. The equation to verify against is $y = 8x - 7$ .

STEP 2

To determine if the point $(7,10)$ is a solution to the equation $y = 8x - 7$ , we need to substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.

STEP 3

Substitute the x-coordinate (which is 7) into the equation.
$y = 8(7) - 7$

STEP 4

Perform the multiplication.
$y = 56 - 7$

STEP 5

Subtract 7 from 56 to find the value of y.
$y = 49$

STEP 6

Now we compare the calculated y-value with the y-coordinate of the given point. If they match, the point is a solution to the equation; if they do not match, the point is not a solution.

STEP 7

The y-coordinate of the given point is 10, which does not match the calculated y-value of 49.
$10 \neq 49$

STEP 8

Since the y-coordinate of the given point does not match the calculated y-value, the point $(7,10)$ is not a solution to the equation $y = 8x - 7$ .
The answer is No.

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Is the point ( $7, 10$ ) a solution to the equation $y = 8x - 7$ ?

STEP 1

Assumptions
1. The given point is $(7,10)$ .
2. The equation to verify against is $y = 8x - 7$ .

STEP 2

To determine if the point $(7,10)$ is a solution to the equation $y = 8x - 7$ , we need to substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.

STEP 3

Substitute the x-coordinate (which is 7) into the equation.
$y = 8(7) - 7$

STEP 4

Perform the multiplication.
$y = 56 - 7$

STEP 5

Subtract 7 from 56 to find the value of y.
$y = 49$

STEP 6

Now we compare the calculated y-value with the y-coordinate of the given point. If they match, the point is a solution to the equation; if they do not match, the point is not a solution.

STEP 7

The y-coordinate of the given point is 10, which does not match the calculated y-value of 49.
$10 \neq 49$

STEP 8

Since the y-coordinate of the given point does not match the calculated y-value, the point $(7,10)$ is not a solution to the equation $y = 8x - 7$ .
The answer is No.

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Is the point (7,107, 107,10) a solution to the equation y=8x−7y = 8x - 7y=8x−7?

STEP 1

Assumptions1. The given point is (7,10)(7,10)(7,10).2. The equation to verify against is y=8x−7y = 8x - 7y=8x−7.

STEP 2

To determine if the point (7,10)(7,10)(7,10) is a solution to the equation y=8x−7y = 8x - 7y=8x−7, we need to substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.

STEP 3

Substitute the x-coordinate (which is 7) into the equation.y=8(7)−7y = 8(7) - 7y=8(7)−7

STEP 4

Perform the multiplication.y=56−7y = 56 - 7y=56−7

STEP 5

Subtract 7 from 56 to find the value of y.y=49y = 49y=49

STEP 6

Now we compare the calculated y-value with the y-coordinate of the given point. If they match, the point is a solution to the equation; if they do not match, the point is not a solution.

STEP 7

The y-coordinate of the given point is 10, which does not match the calculated y-value of 49.10≠4910 \neq 4910=49

STEP 8

Since the y-coordinate of the given point does not match the calculated y-value, the point (7,10)(7,10)(7,10) is not a solution to the equation y=8x−7y = 8x - 7y=8x−7.The answer is No.

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Is the point ( $7, 10$ ) a solution to the equation $y = 8x - 7$ ?

Assumptions
1. The given point is $(7,10)$ .
2. The equation to verify against is $y = 8x - 7$ .

To determine if the point $(7,10)$ is a solution to the equation $y = 8x - 7$ , we need to substitute the x-coordinate of the point into the equation and check if the resulting y-value matches the y-coordinate of the point.

Substitute the x-coordinate (which is 7) into the equation.
$y = 8(7) - 7$

Perform the multiplication.
$y = 56 - 7$

Subtract 7 from 56 to find the value of y.
$y = 49$

The y-coordinate of the given point is 10, which does not match the calculated y-value of 49.
$10 \neq 49$

Since the y-coordinate of the given point does not match the calculated y-value, the point $(7,10)$ is not a solution to the equation $y = 8x - 7$ .
The answer is No.