The problem asks to solve the following system of equations by graphing: $4x + y = 3$ $3x - y = 4$

1. Problem Description

The problem asks to solve the following system of equations by graphing:

$4x + y = 3$

$3x - y = 4$

2. Solution Steps

First, we rewrite each equation in slope-intercept form ($y = mx + b$).

Equation 1: $4x + y = 3$

Subtract $4x$ from both sides:

$y = -4x + 3$

The slope of the first line is $m_1 = -4$ and the y-intercept is $b_1 = 3$.

Equation 2: $3x - y = 4$

Subtract $3x$ from both sides:

$-y = -3x + 4$

Multiply both sides by -1:

$y = 3x - 4$

The slope of the second line is $m_2 = 3$ and the y-intercept is $b_2 = -4$.

To find the intersection point (the solution to the system), we set the two equations equal to each other:

$-4x + 3 = 3x - 4$

Add $4x$ to both sides:

$3 = 7x - 4$

Add 4 to both sides:

$7 = 7x$

Divide both sides by 7:

$x = 1$

Now, substitute $x = 1$ into either equation to find the value of $y$. We'll use the first equation:

$y = -4(1) + 3$

$y = -4 + 3$

$y = -1$

So, the solution is $x = 1$ and $y = -1$.

3. Final Answer

The solution to the system of equations is $(1, -1)$.