How do solve the following linear system?: $4 x - 2 y = 2, x - 3 y = - 2$ $4x-2y=2 , x-3y=-2$ ?

Question

1695 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-07T17:36:51

$solution : x=1 and y=1$ $"solution : x=1 and y=1 "$

$given :$ $"given :"$

$4 x - 2 y = 2 (1)$ $4x-2y=2" (1)"$

$x - 3 y = - 2 (2)$ $x-3y=-2" (2)"$

$expand both side of equation (2) by 4$ $"expand both side of equation (2) by 4 "$

$4 (x - 3 y) = - 2 \cdot 4$ $4(x-3y)=-2*4$

$4 x - 12 y = - 8$ $4x-12y=-8$

$4 x = 12 y - 8 (3)$ $color(red)(4x)=12y-8" (3)"$
$rearrange (1)$ $"rearrange (1)"$

$4 x = 2 y + 2 (4)$ $color(red)(4x)=2y+2" (4)"$

$(3) and (4) are equal.$ $"(3) and (4) are equal."$

$12 y - 8 = 2 y + 2$ $12y-8=2y+2$

$12 y - 2 y = 2 + 8$ $12y-2y=2+8$

$10 y = 10$ $10y=10$

$y = 1$ $y=1$

$now use (1) or (2)$ $"now use (1) or (2)"$

$4 x - 2 \cdot 1 = 2$ $4x-2*1=2$

$4 x - 2 = 2$ $4x-2=2$

$4 x = 2 + 2$ $4x=2+2$

$4 x = 4$ $4x=4$

$x = 1$ $x=1$

How do solve the following linear system?: 4x−2y=2,x−3y=−2 4x-2y=2 , x-3y=-2 ?