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Determine if the point (2, -3) is a solution to the system 2x + 5y = 11 and 3x - 2y = 1

User Orjan
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Part-I: Brief explanation/solution to the problem shown:

Step-1) Determine the value of the x and y variables

To verify if (2, -3) is a solution to the system of equations provided in the question, we will need to determine the value of the x and y variables.

To do this, we will have to compare the coordinates of the point (2, -3) with the "original form" of the coordinate point (x, y). Then, we will have to identify the values (from the coordinates) in their respective order.

Example: (4, 5) = (x, y) ⇒ x = 4; y = 5

Step-2) Substitute the x and y values into one of the equations

The next step is to substitute the value of the variables. This is a required step for the coordinate provided to be verified. Once you substitute the value of the variables, you can move on to the next step process.

Step-3) Simplify the equation completely until it is in simplified form

Then, we will have to simplify the equation completely.

This is also a required step because simplifying is a process where we can convert an expression to a specific numerical value, which can help us create final conclusions to a problem. It can also help us obtain a specific numerical value from any large/small expression provided.

Step-4) Compare both sides and verify if they are equal/not equal

If both sides of the equation do not receive the same value, then the point (2, -3) is not a solution to the provided system of equation.

Part II: Verify if the point is a solution of the equations:

Given Information (Provided in the question):

  • Equation 1: 2x + 5y = 11
  • Equation 2: 3x - 2y = 1

Step-1) Determine the x and y variables from the coordinates:

  • (2, -3) = (x, y) ⇒ x = 2; y = -3

Step-2) Substitute the variables into any equation:

  • ⇒ 2x + 5y = 11
  • ⇒ 2(2) + 5(-3) = 11

Step-3) Simplify both sides of the equation:

  • ⇒ 2(2) + 5(-3) = 11
  • ⇒ 4 + (-15) = 11
  • ⇒ 4 - 15 = 11
  • ⇒ -11 ≠ 11

Therefore, (2, -3) is not a solution to the system of equations.

User NealJMD
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