How to write a system of equations with a given solution?

Question

Can anyone please help me write a system of equations that has (2, 7.5) as its solution? If you don't mind could you please inform me on how you got to the answer? thank you.

Answer 1

y = 2
x = 7.5

y = e^x + c
y = mx + c
y = ln(x) + c
etc...

Answer 2

This is something I do all the time as a teacher, because it's how you get answers that "work out" rather than just stupid decimals.

The person who suggests you put things in y = mx + b form is right, but there's an easier way.

Make both your equations have the form Ax + By = C. Just come up with some coefficients (numbers that will go in front of x and y), and see what happens.

For example you coiuld have:
9x - 2y = ...
and x + 4y = ...

Plug in the numbers you have for x and y, and find out what the answer to each one is.

9(2) - 2(7.5) = 3 and 2 + 4(7.5) = 32

So a system of equations would be
9x - 2y = 3
x + 4y = 32

(By the way, I purposedly chose even numbers for the coefficeints on y, because I knew that the decimal would cancel when 7.5 was multiplied by an even number.)

Answer 3

x= 2, y=7.5
1. Plug in the x and y value into the equation y=mx+b
2. Pick a m or b value.
3. Simplify to find the other m or b value.
4. plug m and b into the y=mx+b equation.
Example: y=x+5.5