How do you solve 6x-2y= - 3 and 5x+3y=4?

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Answer 1 · 2015-09-27T14:31:53

$x = - \frac{1}{28}$ $color(blue)(x=-1/28$

$y = \frac{13}{6}$ $color(blue)(y=13/6$

$6 x - 2 y = - 3$ $6x-2y=-3$ , multiplying this equation by $3$ $3$

$18 x - 6 y = - 9$ $18x-color(blue)(6y)=-9$ .....equation $(1)$ $(1)$

$5 x + 3 y = 4$ $5x+3y=4$ , multiplying this equation by $2$ $2$

$10 x + 6 y = 8$ $10x+color(blue)(6y)=8$ .......equation $(2)$ $(2)$

Solving by elimination.
Adding equation $1$ $1$ and $2$ $2$ to eliminate $6 y$ $color(blue)(6y$

$18x-cancelcolor(blue)(6y)=-9$
$10x+cancelcolor(blue)(6y)=8$

$28x=-1$

$color(blue)(x=-1/28$

Finding $y$ by substituting $x$ in equation $1$

$18x-6y=-9$

$18x +9=6y$

$18*(-1/28) +9=6y$

$-9/14 +9=6y$

$(-9 +126)/9=6y$

$(117)/9=6y$

$13=6y$

$color(blue)(y=13/6$