Fiona wrote the linear equation y = 2/5x – 5. when henry wrote his equation, they discovered that his equation had all the same solutions as fiona’s. which equation could be henry’s?

Hello there!

The equation that Fiona wrote is y = (2/5)*x + 5 and we want to find another equation that has the same solutions.

Let's analyze what things we can change in this equation.

If we change the x-intercept, we get a parallel linear equation to the given by Fiona, and this parallel linear equation will have different solutions.

If we change the slope, the linear equation resultant will intercept the Fiona one in only one point, then these two functions will have different solutions.

Then we cant change the slope or the x-intercept if we want to have all the same solutions, then the only thing we can do is write it in a different way, but not changing it.

The equation is y = (2/5)*x + 5  

we can write the 5 as 25/5, then

y= (2/5)x  25/5 = (1/5)(2x + 25)

now we multiply in both sides by 5.

5y = 2x + 25

this can be an example of Henry's equation.

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.