Question

Solve the system. 7×+2y=-8; 8y=4×

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve the system, let's rearrange the equations:

Equation 1: 7x + 2y = -8

Equation 2: 4x - 8y = 0 (divided both sides by 4)

Next, let's multiply Equation 1 by 4 to eliminate the coefficient of x in equation 2:

4(7x + 2y) = 4(-8)
28x + 8y = -32

Now we have two equations with the same coefficient in x:

Equation 3: 28x + 8y = -32
Equation 2: 4x - 8y = 0

By adding Equation 3 and Equation 2:

(28x + 8y) + (4x - 8y) = -32 + 0
32x = -32

Divide by 32 on both sides of the equation:

x = -32/32
x = -1

Now substitute x = -1 into either equation to solve for y. Let's use Equation 2:

8y = 4(-1)
8y = -4

Divide both sides by 8:

y = -4/8
y = -1/2

Therefore, the solution to the system of equations is x = -1 and y = -1/2.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To solve the given system of equations:

Equation 1: 7x + 2y = -8
Equation 2: 8y = 4x

Step 1: Let's solve equation 2 for x.
Divide both sides of Equation 2 by 4:
8y / 4 = 4x / 4
2y = x

Step 2: Now substitute the value of x from Equation 2 into Equation 1.
7x + 2y = -8
7(2y) + 2y = -8
14y + 2y = -8
16y = -8

Step 3: Divide both sides of the equation by 16 to solve for y:
16y / 16 = -8 / 16
y = -1/2

Step 4: Now substitute the value of y back into Equation 2 to solve for x:
8y = 4x
8(-1/2) = 4x
-4 = 4x

Step 5: Divide both sides of the equation by 4 to solve for x:
-4 / 4 = 4x / 4
-1 = x

Therefore, the solution to the system of equations is x = -1 and y = -1/2.