Question

1. 8x + 14y = 4

-6x - 7y = -10

Explanation:

Step1: Multiply the second equation by 2

To eliminate \( y \), we multiply the second equation \(-6x - 7y = -10\) by 2. This gives us:
\( 2\times(-6x - 7y)=2\times(-10) \)
\( -12x - 14y = -20 \)

Step2: Add the new equation to the first equation

Now we add the first equation \( 8x + 14y = 4 \) to the new equation \( -12x - 14y = -20 \):
\( (8x + 14y)+(-12x - 14y)=4+(-20) \)
Simplifying the left side: \( 8x - 12x + 14y - 14y=-4x \)
Simplifying the right side: \( 4 - 20=-16 \)
So we have \(-4x=-16\)

Step3: Solve for \( x \)

Divide both sides of \(-4x = -16\) by \(-4\):
\( x=\frac{-16}{-4}=4 \)

Step4: Substitute \( x = 4 \) into the first equation to solve for \( y \)

Substitute \( x = 4 \) into \( 8x + 14y = 4 \):
\( 8\times4+14y = 4 \)
\( 32+14y = 4 \)
Subtract 32 from both sides: \( 14y=4 - 32=-28 \)
Divide both sides by 14: \( y=\frac{-28}{14}=-2 \)

Answer:

\( x = 4 \), \( y = -2 \)