We are given a system of two linear equations with two variables, $x$ and $y$. The equations are: $2x + 5y = 24$ $4x + 3y = 20$ We are asked to solve for $x$ and $y$ using the elimination method.

1. Problem Description

We are given a system of two linear equations with two variables, $x$ and $y$. The equations are:

$2x + 5y = 24$

$4x + 3y = 20$

We are asked to solve for $x$ and $y$ using the elimination method.

2. Solution Steps

We can eliminate $x$ by multiplying the first equation by $-2$ and then adding the result to the second equation.

Multiply the first equation by $-2$:

$-2(2x + 5y) = -2(24)$

$-4x - 10y = -48$

Now add this to the second equation:

$(-4x - 10y) + (4x + 3y) = -48 + 20$

$-4x - 10y + 4x + 3y = -28$

$-7y = -28$

Divide both sides by $-7$:

$y = \frac{-28}{-7}$

$y = 4$

Now substitute $y = 4$ into the first equation to solve for $x$:

$2x + 5(4) = 24$

$2x + 20 = 24$

$2x = 24 - 20$

$2x = 4$

$x = \frac{4}{2}$

$x = 2$

3. Final Answer

The solution to the system of equations is $x = 2$ and $y = 4$.