Question

How would you solve 2x+7y=14?

Answer 1

Hello there!

Answer:
`\boxed{\bf\left \{ {{y=1} \atop {x=-3.5}} \right. }`

How?

Both x and y are variables. And with these both variables, we need to find which function would work with both 2 and 7, in order for it to have an answer of 14.

We would first want to rearrange by subtracting.

`2*x+7*y-(14)=0 \\ \\ \sf Solve: 2x+7y-14 = 0 \\ \\`

We are going to use a formula that I use with these kind of problem, which this would make us how far the Y goes on the grid. It will tell us how far X with go along the grid line also. M would show us how the slope or gradient goes either up or down. And B is the y-intercept. Which shows us where the line goes on the y -axis.

And with this in mind, we can graph the line, which, this is the way I would do it, to get into more in detail with this math problem.

`\bf (y) \\ \\ |-2.000\\|\\|\\|\ \ \ y-intercept\ \ \|-- \ rise(es)\\|------ \ \ \ \|-- lower(ing) \ down \ by \ (3.500)\\|\\|\\|-0.000\\|-------------------------- \ \ \ \ \ \ \ \ \ \bf (x)\\|-\bf x-intercept ; x=7.000`

So, now that we have that covered, we have the line demonstrated. We see that y=7.000, and x= -3.500

Therefore, we then do 2 × -3.5 = 7; or in other words, 7.000 (which is exactly what we need.)

Then for the y-intercept, it would be a little different.

`y-intercept = 14/7 = 2` (which in other terms, 2.000) which is also what we need to see.

If you had noticed, all this math we're doing, is all being seen back within the little grid line we had done above.

`2x*-3\\ ( \ \ \ \ \ \ \ \ ) \\ \ \ \ \ - ( \ \ )-\\ \\ \ \ \ \ \sf 7 \ is \ the \ answer`

Therefore, your answer would be the following underneath.

ANSWER:
`\bf{\left[\begin{array}{ccc}\bf \boxed{\bf \left \{ {{y=1} \atop {x=-3.5}} \right.}\end{array}\right] }`