Question

1. $y = 3x - 10$ $y = 5x - 14$

Explanation:

Step1: Set the two equations equal

Since both equations are solved for \( y \), we can set them equal to each other: \( 3x - 10 = 5x - 14 \)

Step2: Subtract \( 3x \) from both sides

\( 3x - 3x - 10 = 5x - 3x - 14 \) simplifies to \( -10 = 2x - 14 \)

Step3: Add 14 to both sides

\( -10 + 14 = 2x - 14 + 14 \) simplifies to \( 4 = 2x \)

Step4: Divide both sides by 2

\( \frac{4}{2} = \frac{2x}{2} \) gives \( x = 2 \)

Step5: Substitute \( x = 2 \) into the first equation

Substitute \( x = 2 \) into \( y = 3x - 10 \): \( y = 3(2) - 10 = 6 - 10 = -4 \)

Wait, there was a mistake in the handwritten work. Let's correct it.

Step1: Set equations equal

\( 3x - 10 = 5x - 14 \)

Step2: Subtract \( 3x \) from both sides

\( -10 = 2x - 14 \)

Step3: Add 14 to both sides

\( 4 = 2x \)

Step4: Solve for \( x \)

\( x = 2 \)

Step5: Find \( y \)

Using \( y = 3x - 10 \), \( y = 3(2) - 10 = -4 \). So the solution is \( (2, -4) \)

But let's follow the correct steps:

Step1: Equate the two expressions for \( y \)

Given \( y = 3x - 10 \) and \( y = 5x - 14 \), we have \( 3x - 10 = 5x - 14 \)

Step2: Isolate \( x \) terms

Subtract \( 3x \) from both sides: \( -10 = 2x - 14 \)

Step3: Isolate constant terms

Add 14 to both sides: \( 4 = 2x \)

Step4: Solve for \( x \)

Divide both sides by 2: \( x = 2 \)

Step5: Substitute \( x \) to find \( y \)

Substitute \( x = 2 \) into \( y = 3x - 10 \): \( y = 3(2) - 10 = 6 - 10 = -4 \)

Answer:

The solution to the system of equations is \( (2, -4) \)