Question

How do you solve the following system: `-2x + 5y = 20, 2x-y=7`?

Answer 1

`(55/8,27/4)`

Explanation:

`color(red)(-2x)+5y=20to(1)`

`color(red)(2x)-y=7to(2)`

`" the system is probably best solved using "color(blue)"elimination method"`

`"since the x terms have the same numeric value but with"`
`"opposing signs, adding them will eliminate the x term"`

`(1)+(2)" term by term"`

`(-2x+2x)+(5y-y)=(20+7)`

`rArr4y=27`

`"divide both sides by 4"`

`(cancel(4) y)/cancel(4)=27/4`

`rArry=27/4`

`"substitute this value into either " (1)" or " (2)`

`2x-27/4=7larr" substituting in " (2)`

`rArr2x=7+27/4=55/4`

`rArrx=55/8`

`color(blue)"As a check"`

Substitute these values in ( 1 )

`-2(55/8)+5(27/4)=-55/4+135/4=20rarr" True"`

`rArr"point of intersection" =(55/8,27/4)`