Question

How do you solve the following system: #4x + y = -1 , 2x+7y=1 #?

Answer 1

`x=-4/13 and y=3/13`

Explanation:

Since you have 2 simultaneous equations and two variable you know that this system has unique solutions (this just means it has a solution). You can do it 2 different ways. One method would be to add/subtract multiples of the equations to remove a variable and then solve for the other. once you know one variable you can substitute it into an equation to find the other variable. The other method (which I prefer) is to rearrange on an equation in terms of a variable.
For example, take the first equation and rearrange it in terms of y

`y=-1-4x`

Then substitute this into the first equation

`2x+7(-1-4x)=1`

`2x-7-28x=1`

`-26x=8`

`x=8/26`

`x=-4/13`

now just substitute this value of x into the first equation to find y

`y=-1-4(-4/13)`
`y=3/13`