1.) solve by elimination:\n$5x - 3y = 23$\n$2x - 2y = 2$

Explanation:

Step1: Simplify the second equation

Divide the second equation by 2: $x - y = 1$ Rearrange to get $x = y + 1$

Step2: Eliminate $x$ in first equation

Substitute $x = y + 1$ into $5x - 3y = 23$: $5(y + 1) - 3y = 23$ Expand: $5y + 5 - 3y = 23$ Combine like terms: $2y + 5 = 23$

Step3: Solve for $y$

Subtract 5 from both sides: $2y = 23 - 5$ $2y = 18$ Divide by 2: $y = 9$

Step4: Solve for $x$

Substitute $y = 9$ into $x = y + 1$: $x = 9 + 1 = 10$

Answer:

$x = 10$, $y = 9$