How do you solve $5 x + y = 5$ $5x+y=5$ and $3 x + 2 y = 3$ $3x+2y=3$ using substitution?

Question

2522 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-21T19:24:20

$x = 1 and y = 2$ $x=1 and y=2$

$5 x + y + (- 5 x) = 5 + (- 5 x)$ $" "5x+y+(−5x)=5+(−5x)" "$ (Add $- 5 x$ $-5x$ to both sides)

$y = - 5 x + 5$ $" "y=−5x+5$ .

Substitute $(- 5 x + 5)$ $color(blue)((−5x+5))$ for $y in 3 x + 2 y = 3$ $color(blue)(y) " in " 3x+2y=3$ :

$3 x + 2 y = 3$ $" "3x+2color(blue)(y)=3$

$3 x + 2 (- 5 x + 5) = 3$ $3x+2color(blue)((−5x+5))=3$

$3 x - 10 x + 10 = 3$ $3x-10x+10 =3$

$- 7 x + 10 = 3$ $−7x+10=3$

$- 7 x + 10 + (- 10) = 3 + (- 10)$ $−7x+10+ (−10)=3+(−10)" "$ (Add $- 10$ $-10$ to both sides)

$- 7 x = - 7$ $−7x=−7$

$\frac{7 x}{- 7} = \frac{- 7}{- 7}$ $(7x)/-7=(-7)/-7" "$ (Divide both sides by $- 7$ $-7$ )

$x = 1 .$ $x =1.$

Substitute $1$ $1$ for $x$ $x$ in $y = - 5 x + 5$ $y=−5x+5$

$y = - 5 x + 5$ $y=−5x+5$

$y = (- 5) (1) + 5$ $y=(−5)(1)+5$

$y = 0$ $y=0" "$ (Simplify both sides of the equation).

How do you solve 5x+y=55x+y=55x+y=5 and 3x+2y=33x+2y=33x+2y=3 using substitution?