Final answer:
To pair an equation with 4x-3y=10 where (1, -2) is the solution, we can use the point-slope form. By substituting the point into this form and choosing a different slope from the first equation, we can derive y = 2x - 4, ensuring that the two lines intersect only at (1, -2).
Step-by-step explanation:
To write an equation that can be paired with 4x-3y=10 to form a system that has (1,-2) as the only solution, we need to find an equation of a line that also passes through the point (1,-2).
Given that the point (1,-2) is the solution, it must satisfy the equation we are looking for.
Therefore, we can use the point-slope form of the equation of a line, which is (y - y1) = m(x - x1) where m is the slope and (x1, y1) is the point through which the line passes.
Since the point (1, -2) is given, we plug x1 = 1 and y1 = -2 into the point-slope form. We can choose any non-zero slope m that is different from the slope of the given equation 4x-3y=10, which is 4/3. If we take m=2 as an example, our equation is: (y + 2) = 2(x - 1)
Expanding this, we get:
y + 2 = 2x - 2
Then, by subtracting 2 from both sides, we have:
y = 2x - 4
This new equation, when paired with 4x-3y=10, forms a system with (1, -2) as the only solution because it intersects at that point without being parallel or identical to the first equation.