Question

How do you solve the following system using substitution?: `5x+2y=-4, -3x+y=20`

Answer 1

`(x,y)to(-4,8)`

Explanation:

`5x+2y=-4to(1)`

`-3x+y=20to(2)`

`"rearrange equation "(2)" to express y in terms of x"`

`"add "3x" to both sides"`

`rArry=20+3xto(3)`

`color(blue)"substitute "y=20+3x" into equation "(1)`

`5x+2(20+3x)=-4larr"distribute"`

`rArr5x+40+6x=-4`

`rArr11x+40=-4`

`"subtract 40 from both sides"`

`rArr11x=-44`

`"divide both sides by 11"`

`rArrx=(-44)/11=-4`

`"substitute "x=-4" into equation "(3)`

`rArry=20-12=8`

`"the point of intersection "=(-4,8)`

Answer 2

The solutions are `{x=-4 ; y=8}`

Explanation:

The equations are

`{(5x+2y=-4),(-3x+y=20):}`

`<=>`, `{(5x+2y=-4),(y=3x+20):}`

`<=>`, `{(5x+2(3x+20)=-4),(y=3x+20):}`

`<=>`, `{(11x+40=-4),(y=3x+20):}`

`<=>`, `{(11x=-44),(y=3x+20):}`

`<=>`, `{(x=-4),(y=3xx-4+20=8):}`