Question

How do you solve this system of equations: `2x + 4y = 9; 5x - y = - \frac { 21} { 2}`?

Answer 1

`(x,y)to(-3/2,3)`

Explanation:

`2x+4y=9to(1)`

`5x-y=-21/2to(2)`

`"multiply equation "(2)" by 4"`

`"this will make the coefficients of y opposites so we can"`
`"add the equations and eliminate the y term"`

`rArr20x-4y=-42to(3)`

`"add equations "(1)" and "(3)" term by term to eliminate y"`

`(2x+20x)+(cancel(4y-4y)^0)=(9-42)`

`rArr22x=-33`

`"divide both sides by 22"`

`(cancel(22) x)/cancel(22)=(-33)/22`

`rArrx=-3/2`

`"substitute "x=-3/2" in equation "(1)" and solve for y"`

`-3+4y=9`

`"add 3 to both sides"`

`cancel(-3)cancel(+3)+4y=9+3`

`rArr4y=12`

`"divide both sides by 4"`

`(cancel(4) y)/cancel(4)=12/4`

`rArry=3`

`"the point of intersection is "(-3/2,3)`
graph{(y+1/2x-9/4)(y-5x-21/2)((x+3/2)^2+(y-3)^2-0.04)=0 [-10, 10, -5, 5]}