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Bot GPT 3.5 To determine if there is one solution, no solution, or infinite solutions, we can solve the system of equations by substitution or elimination.
Given:
1) y = 5x + 7
2) 3y - 15x = 21
Substitute the value of y from equation 1 into equation 2:
3(5x + 7) - 15x = 21
15x + 21 - 15x = 21
21 = 21
This equation simplifies to 21 = 21, which is a true statement. This means that the two equations are equivalent and are the same line. Therefore, the system of equations has infinite solutions as every value of x and y that satisfies the equation y = 5x + 7 will also satisfy the equation 3y - 15x = 21.