Math / Algebra

QuestionIs $(1,8)$ a solution to this system of inequalities? $\begin{array}{l} y>x+7 \\ y \geq 6 x+2 \end{array}$ yes no

Studdy Solution

STEP 1

1. We have a system of two inequalities.
2. We need to check if the point $(1,8)$ satisfies both inequalities simultaneously.

STEP 2

1. Substitute the point $(1,8)$ into the first inequality and check if it holds.
2. Substitute the point $(1,8)$ into the second inequality and check if it holds.
3. Determine if $(1,8)$ is a solution to the system based on the results from the previous steps.

STEP 3

Substitute the point $(1,8)$ into the first inequality $y > x + 7$ .
Given: $y = 8$ $x = 1$
Substitute: $8 > 1 + 7$ $8 > 8$
The inequality does not hold because $8$ is not greater than $8$ .

STEP 4

Substitute the point $(1,8)$ into the second inequality $y \geq 6x + 2$ .
Given: $y = 8$ $x = 1$
Substitute: $8 \geq 6(1) + 2$ $8 \geq 6 + 2$ $8 \geq 8$
The inequality holds because $8$ is equal to $8$ .

STEP 5

Determine if $(1,8)$ is a solution to the system.
Since $(1,8)$ does not satisfy the first inequality, it is not a solution to the system of inequalities.
The answer is $\boxed{\text{no}}$ .

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QuestionIs $(1,8)$ a solution to this system of inequalities? $\begin{array}{l} y>x+7 \\ y \geq 6 x+2 \end{array}$ yes no

Studdy Solution

STEP 1

1. We have a system of two inequalities.
2. We need to check if the point $(1,8)$ satisfies both inequalities simultaneously.

STEP 2

1. Substitute the point $(1,8)$ into the first inequality and check if it holds.
2. Substitute the point $(1,8)$ into the second inequality and check if it holds.
3. Determine if $(1,8)$ is a solution to the system based on the results from the previous steps.

STEP 3

Substitute the point $(1,8)$ into the first inequality $y > x + 7$ .
Given: $y = 8$ $x = 1$
Substitute: $8 > 1 + 7$ $8 > 8$
The inequality does not hold because $8$ is not greater than $8$ .

STEP 4

Substitute the point $(1,8)$ into the second inequality $y \geq 6x + 2$ .
Given: $y = 8$ $x = 1$
Substitute: $8 \geq 6(1) + 2$ $8 \geq 6 + 2$ $8 \geq 8$
The inequality holds because $8$ is equal to $8$ .

STEP 5

Determine if $(1,8)$ is a solution to the system.
Since $(1,8)$ does not satisfy the first inequality, it is not a solution to the system of inequalities.
The answer is $\boxed{\text{no}}$ .

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QuestionIs (1,8)(1,8)(1,8) a solution to this system of inequalities? y>x+7y≥6x+2\begin{array}{l} y>x+7 \\ y \geq 6 x+2 \end{array}y>x+7y≥6x+2​ yes no

Studdy Solution

STEP 1

1. We have a system of two inequalities.2. We need to check if the point (1,8)(1,8)(1,8) satisfies both inequalities simultaneously.

STEP 2

1. Substitute the point (1,8)(1,8)(1,8) into the first inequality and check if it holds.2. Substitute the point (1,8)(1,8)(1,8) into the second inequality and check if it holds.3. Determine if (1,8)(1,8)(1,8) is a solution to the system based on the results from the previous steps.

STEP 3

Substitute the point (1,8)(1,8)(1,8) into the first inequality y>x+7y > x + 7y>x+7.Given: y=8 y = 8 y=8 x=1 x = 1 x=1Substitute: 8>1+7 8 > 1 + 7 8>1+7 8>8 8 > 8 8>8The inequality does not hold because 888 is not greater than 888.

STEP 4

Substitute the point (1,8)(1,8)(1,8) into the second inequality y≥6x+2y \geq 6x + 2y≥6x+2.Given: y=8 y = 8 y=8 x=1 x = 1 x=1Substitute: 8≥6(1)+2 8 \geq 6(1) + 2 8≥6(1)+2 8≥6+2 8 \geq 6 + 2 8≥6+2 8≥8 8 \geq 8 8≥8The inequality holds because 888 is equal to 888.

STEP 5

Determine if (1,8)(1,8)(1,8) is a solution to the system.Since (1,8)(1,8)(1,8) does not satisfy the first inequality, it is not a solution to the system of inequalities. The answer is no\boxed{\text{no}}no​.

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QuestionIs $(1,8)$ a solution to this system of inequalities? $\begin{array}{l} y>x+7 \\ y \geq 6 x+2 \end{array}$ yes no

1. We have a system of two inequalities.
2. We need to check if the point $(1,8)$ satisfies both inequalities simultaneously.

1. Substitute the point $(1,8)$ into the first inequality and check if it holds.
2. Substitute the point $(1,8)$ into the second inequality and check if it holds.
3. Determine if $(1,8)$ is a solution to the system based on the results from the previous steps.

Substitute the point $(1,8)$ into the first inequality $y > x + 7$ .
Given: $y = 8$ $x = 1$
Substitute: $8 > 1 + 7$ $8 > 8$
The inequality does not hold because $8$ is not greater than $8$ .

Substitute the point $(1,8)$ into the second inequality $y \geq 6x + 2$ .
Given: $y = 8$ $x = 1$
Substitute: $8 \geq 6(1) + 2$ $8 \geq 6 + 2$ $8 \geq 8$
The inequality holds because $8$ is equal to $8$ .

Determine if $(1,8)$ is a solution to the system.
Since $(1,8)$ does not satisfy the first inequality, it is not a solution to the system of inequalities.
The answer is $\boxed{\text{no}}$ .