# solve and check x + y = -2; y = 4x - 7

solve for y and x intercepts.

Substitution Method :

The system of equations are x + y = - 2 and y = 4x - 7.

Step 1 : The equation 2 : y = 4x - 7 is already solved for y.

Step 2 : Substitute 4x - 7 for y in the equation 1 : x + y = - 2 to find the value of x.

x + (4x - 7) = - 2

5x - 7 = - 2

5x - 7 + 7 = - 2 + 7

5x = 5

Divide each side by 5.

5x/5 = 5/5

x = 1.

Step 3 : Substitute 1 for x in either equation to find y.

Equation 2 : y = 4x - 7

y = 4(1) - 7

y = - 3.

The solution (x, y) = (1, - 3).

CHECK :

To check the solution, substitute (x, y) = (1, - 3) in each original equation.

Equation 1 : x + y = - 2     |   Equation 2 : y = 4x - 7

(1) + (- 3) ≟ - 2    |                 (- 3) ≟ 4(1) - 7

- 2 = - 2    |                     - 3 = - 3
The text passage contains a mathematical problem involving solving a system of linear equations and checking the solution. It provides a detailed step-by-step solution to the problem.
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Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
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- MULTIPLE_QUESTIONS
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system
# solve and check x + y = -2; y = 4x - 7

solve for y and x intercepts.

Substitution Method :

The system of equations are x + y = - 2 and y = 4x - 7.

Step 1 : The equation 2 : y = 4x - 7 is already solved for y.

Step 2 : Substitute 4x - 7 for y in the equation 1 : x + y = - 2 to find the value of x.

x + (4x - 7) = - 2

5x - 7 = - 2

5x - 7 + 7 = - 2 + 7

5x = 5

Divide each side by 5.

5x/5 = 5/5

x = 1.

Step 3 : Substitute 1 for x in either equation to find y.

Equation 2 : y = 4x - 7

y = 4(1) - 7

y = - 3.

The solution (x, y) = (1, - 3).

CHECK :

To check the solution, substitute (x, y) = (1, - 3) in each original equation.

Equation 1 : x + y = - 2     |   Equation 2 : y = 4x - 7

(1) + (- 3) ≟ - 2    |                 (- 3) ≟ 4(1) - 7

- 2 = - 2    |                     - 3 = - 3
user
The text passage contains a mathematical problem involving solving a system of linear equations and checking the solution. It provides a detailed step-by-step solution to the problem.

TYPE: SINGLE_QUESTION_WITH_ANSWER