Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t

Question

Art

10 days ago

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Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t

he other is quadratic–without graphing the system of equations.

Mathematics

1 answer:

babunello [3.6K] · Answer 1 · 2026-02-23T17:48:55+03:00

Answer:

To find the number of genuine solutions for a system of equations consisting of a linear equation and a quadratic equation

1) With two variables, say x and y, rearrange the linear equation to express y, then substitute this y in the quadratic equation

After that, simplify the resulting equation and determine the number of real roots utilizing the quadratic formula, $x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}$ for equations of the type 0 = a·x² - b·x + c.

When b² exceeds 4·a·c, two real solutions emerge; if b² equals 4·a·c, there will be a single solution.

Step-by-step explanation:

Explain how you can determine the number of real number solutions of a system of equations in which one equation is linear and t

Reducing

Rearranging the components:

Finding the solution

Isolating the variable 'x'.

Shift all terms with x to one side,

Summing up similar items:

Summing similar items:

Split each side by '9'

Simplifying