Expert answers to "To calculate: The solution for the system of..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

kdgg0909gn

Answered question

2021-11-15

To calculate: The solution for the system of equations

2 x^{2} - x y = 24

and

x^{2} + 3 x y = - 9

Answer & Explanation

huckelig75

Beginner2021-11-16Added 11 answers

Formula used:
Solving a System of Equations using Substitution Method:
Step 1: Consider the first provided equation and calculate the value of one variable in terms of the other.
Step 2: Substitute the value of the variable obtained into the second equation and solve for the variable left.
Step 3: Now substitute the value of the variable obtained into any one equation and compute the second variable.
Consider the provided system of equations:

2 x^{2} - x y = 24

x^{2} + 3 x y = - 9

Multiply

2 x^{2} - x y = 24

with 3, then:

6 x^{2} - 3 x y = 72

x^{2} + 3 x y = - 9

Add both the equations:

7 x^{2} = 63

x^{2} = 9

x = \pm \sqrt{9}

(Divide both sides by 7)

x = \pm 3

Substitute 3 for x in

2 x^{2} - x y = 24

2 {(3)}^{2} - 3 y = 24

18 - 3 y = 24

- 3 y = 6

(Subtract 18 from both sides then divide by —3)

y = - 2

Which is true.
And,

{(3)}^{2} + 3 (3) (- 2) - 9

9 - 18 - 9

- 9 - 9

Which is true.
Thus, solution is verified for (3, -2).
Substitute (-3, 2) in:

2 x^{2} - x y = 24

x^{2} + 3 x y = - 9

Then,

2 {(- 3)}^{2} - (- 3) (2) 24

2 (9) + 624

18 + 624

2424

Which is true.
And,

{(- 3)}^{2} + 3 (- 3) (2) - 9

9 - 18 - 9

- 9 - 9

Which is true.
Thus, solution is verified for (—3,2).
Therefore, the solution for the system of equations

2 x^{2} - x y = 24

and

x^{2} + 3 x y = - 9

{(3, - 2), (- 3, 2)}

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