Question

Construct a system of equations with three equations whose solution is (-2,4,7)

Answer 1

To create a system of equations with the solution (-2,4,7), construct three linear equations with coefficients and constants that satisfy the given solution. Use different coefficients for each equation, ensuring that the solution to the system will coincide with the provided values.

Step-by-step explanation:

To construct a system of equations with the solution (-2,4,7), you will need to create three different equations that have these values as the solution for the variables x, y, and z respectively. Here are the steps to construct such a system:

1. Select arbitrary coefficients for each variable in the equation and an arbitrary constant that will make the equation true when (-2, 4, 7) is substituted in. For instance, for the first equation, using coefficients 1, 2, and -3 for x, y, and z respectively, the constant would be 1*(-2) + 2*4 + (-3)*7 = -11.
2. Create the second equation using a different set of coefficients, for example, 2, -1, and 4, which gives us a constant of 2*(-2) - 4 + 4*7 = 24.
3. Finally, construct the third equation with another set of coefficients, such as 3, -2, and 1, resulting in a constant of 3*(-2) - 2*4 + 1*7 = -6.

Now we have our system of equations:

• x + 2y - 3z = -11
• 2x - y + 4z = 24
• 3x - 2y + z = -6

This system will have (-2, 4, 7) as its unique solution when you solve it using methods such as substitution, elimination, or matrix operations.