We are solving the system of equations:

1. $y - 6x + 17 = 0$
2. $4x + y - 3 = 0$

Step 1: Rewrite both equations in standard form

1. $y = 6x - 17$ (from equation 1)
2. $y = -4x + 3$ (from equation 2)

Step 2: Set the expressions for $y$ equal to each other

Since both equations equal $y$, we can equate them: $6x - 17 = -4x + 3$

Step 3: Solve for $x$

$6x + 4x = 3 + 17$ $10x = 20$ $x = 2$

Step 4: Substitute $x = 2$ into one of the original equations

Using equation 1 ($y = 6x - 17$): $y = 6(2) - 17$ $y = 12 - 17$ $y = -5$

Final Solution

The solution to the system is: $x = 2, \, y = -5$

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Related Questions:

1. How do you solve simultaneous equations graphically?
2. What are the methods for solving simultaneous equations with three variables?
3. Can simultaneous equations always be solved algebraically?
4. What is the geometric interpretation of simultaneous linear equations?
5. How do we use substitution vs elimination methods effectively?

Tip:

For quick checks, always substitute your solution back into both original equations to verify correctness!