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Bot GPT 3.5 To solve this system of equations, we can use the method of substitution or elimination.
Method of Substitution:
1) From the first equation, we have 3x - y = 19.
Rearranging this equation, we get y = 3x - 19.
2) Substitute this value of y into the second equation.
3x - 4(3x - 19) = -5
Simplifying this equation, we get:
3x - 12x + 76 = -5
-9x + 76 = -5
-9x = -81
Dividing both sides by -9, we get:
x = 9.
3) Substitute this value of x back into the first equation:
3(9) - y = 19
27 - y = 19
Subtracting 27 from both sides, we get:
-y = -8
Dividing both sides by -1, we have:
y = 8.
4) Therefore, the solution to the system of equations is x = 9, y = 8.
Method of Elimination:
1) Multiply the first equation by 4 and the second equation by 1 to get:
12x - 4y = 76
3x - 4y = -5
2) Subtract the second equation from the first equation to eliminate y:
12x - 3x - 4y + 4y = 76 - (-5)
9x = 81
Dividing both sides by 9, we get:
x = 9.
3) Substitute this value of x back into the second equation:
3(9) - 4y = -5
27 - 4y = -5
Subtracting 27 from both sides, we get:
-4y = -32
Dividing both sides by -4, we have:
y = 8.
4) Therefore, the solution to the system of equations is x = 9, y = 8.
Both methods yield the same solution: x = 9, y = 8.