How do you solve the following system: $x + 4y = -2 , 5x - 7y = 12$ ?

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Answer 1 · 2015-12-09T17:59:51

The solution for the system of equations is

$color(blue)(x=-142/27, y=22/27$

$x+4y=-2$ , multiplying the equation by $5$
$color(blue)(5x)+20y=-10$ ....equation $(1)$

$color(blue)(5x) -7y=12$ .............equation $(2)$

Solving by elimination :

Subtracting equation $2$ from $1$

$cancelcolor(blue)(5x)+20y=-10$

$cancelcolor(blue)(-5x) +7y=-12$

$27y=-22$

$color(blue)(y=22/27$

Finding $x$ by substituting $y$ in equation $1$ :
$x+4y=-2$

$x=-2-4y$

$x=-2-4 * (22/27)$

$x=-2-(88/27)$

$x=-54/27-(88/27)$

$color(blue)(x=-142/27$

How do you solve the following system: x + 4y = -2 , 5x - 7y = 12 x + 4y = -2 , 5x - 7y = 12 ?