To solve the system of equations 5x + y = 9 and 3x + 2y = 4, we can use either the substitution method or the elimination method. Here, we’ll use the substitution method for clarity.
1. **Rearranging the First Equation**: Start by rearranging the first equation to express one variable in terms of the other. Let’s solve for y in terms of x:
y = 9 - 5x
2. **Substituting into the Second Equation**: Substitute this expression for y into the second equation:
3x + 2(9 - 5x) = 4
3. **Simplifying the Equation**: Now, distribute and simplify:
3x + 18 - 10x = 4
-7x + 18 = 4
4. **Isolating the Variable**: Next, isolate x:
-7x = 4 - 18
-7x = -14
x = 2
5. **Finding the Value of y**: Now that we have x, substitute it back into the rearranged first equation to find y:
y = 9 - 5(2)
y = 9 - 10
y = -1
6. **Conclusion**: The solution to the system of equations is:
x = 2, y = -1
Thus, the coordinates (x, y) are (2, -1). You can also verify this solution by plugging these values back into the original equations to ensure they hold true.