Question

A system of equations is given below.
2x + 7y = 1
-3x – 4y = 5

Create an equivalent system of equations by replacing the first equation by multiplying the first equation by an integer other than 1, and adding it to the second equation.
Use any method to solve the equivalent system of equations (the new first equation with the original second equation).
Prove that the solution for the equivalent system is the same as the solution for the original system of equations.

Answer 1

multiply the 1st equation by an integer, say 2 or 3..

Answer 2

3(2x)+3(7y)=3(1)
6x+21y=3
if you multiply the 2nd equation by 2 when you add them the x term will cancel out, then you can solve for y

Answer 3

this works because you're not changing the equations of the system, you're just scaling them, like the fraction 4/5 is the same as 8/10 or 12/15

Answer 4

So would it be 17y = 8?

Answer 5

@lucaz