Which of these strategies would eliminate a variable in the system of equations?
{
−
x
+
6
y
=
8
7
x
−
y
=
−
2

⎩
⎪
⎪
⎨
⎪
⎪
⎧


−x+6y=8
7x−y=−2


choose all answers that apply:
choose all answers that apply:

(choice a)
a
multiply the bottom equation by
6
66, then subtract the bottom equation from the top equation.

(choice b)
b
add the equations.

(choice c, checked)
c
multiply the top equation by
7
77, then add the equations.

Choice C

Step-by-step explanation:

Choice C - Multiply the top equation by  7 , then add the equations.

Step-by-step explanation:

The question before us is a simultaneous equation with two variables (x and y). Simultaneous equations can be solved using the substitution and elimination method. In this method, one variable is made the subject of the first equation and then it is substituted into the second eqation and the simultaneous equation then becomes solvable by simple arithmetic (eliminating one of the variables)

−x + 6y = 8             ··············· Eqn 1

7x − y = −2            ··············· Eqn 2

Choice A

Multiply bottom equation (Eqn 2) by 6, we have:

6(7x − y = −2 ) ⇒  42x - 6y = -12

then subtract the bottom equation from the top equation, we have:

−x + 6y = 8  - (42x - 6y = -12) ⇒ -43x + 12y = 20

Conclusion: no variable is eliminated, therefore, Choice A is not the answer

Choice B

Add the equations, we have:

−x + 6y = 8  + (7x − y = −2) ⇒ 6x + 5y = 6

Conclusion: no variable is eliminated, therefore, Choice B is not the answer

Choice C

Multiply the top equation (Eqn 1) by 7, we have:

7(−x + 6y = 8 ) ⇒ -7x + 42y = 56

then add the equations, we have:

-7x + 42y = 56 + (7x − y = −2) ⇒ 41y = 54

Conclusion: x variable is eliminated, therefore, Choice C is the answer

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15