The problem requires solving a system of two linear equations with two variables, $x$ and $y$, using the elimination method. The given system is: $3x + 4y = 18$ $2x - 3y = 29$ The problem asks us to find the values of $x$ and $y$ that satisfy both equations.

1. Problem Description

The problem requires solving a system of two linear equations with two variables, $x$ and $y$, using the elimination method. The given system is:

$3x + 4y = 18$

$2x - 3y = 29$

The problem asks us to find the values of $x$ and $y$ that satisfy both equations.

2. Solution Steps

Step 1: Elimination Method

Multiply the first equation by 3:

$3(3x + 4y) = 3(18)$

$9x + 12y = 54$

Multiply the second equation by 4:

$4(2x - 3y) = 4(29)$

$8x - 12y = 116$

Add the two resulting equations:

$(9x + 12y) + (8x - 12y) = 54 + 116$

$17x = 170$

Solve for x:

$x = \frac{170}{17}$

$x = 10$

Step 2: Substitute to solve for y

Substitute the value of $x$ into the first original equation:

$3(10) + 4y = 18$

$30 + 4y = 18$

$4y = 18 - 30$

$4y = -12$

$y = \frac{-12}{4}$

$y = -3$

Step 3: Write the solution as a coordinate pair

The solution is $(x, y) = (10, -3)$.

3. Final Answer

(x, y) = (10, -3)