Question

Write the linear system:

C) Solve the system using substitution and then elimination. Show all work and

steps:


D) List the three parameter values: ab c == = _______ ________ ________


E) Write the quadratic equation: _______

Answer 1

(See explanation for further details).

Explanation:

C) The linear system is:

`(-1)^(2) \cdot a + (-1)\cdot b + c = 5`

`c = - 4`

`(4)^(2)\cdot a + (4)\cdot b + c = 0`

After some algebraic handling:

`a - b + c = 5`

`c = -4`

`16\cdot a + 4\cdot b + c = 0`

By direct substitution:

`a - b - 4 = 5`

`16\cdot a + 4\cdot b - 4 = 0`

`a - b = 9`

`4\cdot a + b = 1`

`a = 9 + b`

`4\cdot (9+b)+b = 1`

`36 + 5\cdot b = 1`

`5\cdot b = -35`

`b = -7`

`a = 2`

D) The parameter values are:
`a = 2`,
`b = -7`,
`c = -4`

E) The quadratic equation is
`y = 2\cdot x^(2) - 7\cdot x -4`