How do you solve the system of equations: 4x+3y=7 and -2x+y=9?

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Answer 1 · 2015-08-08T06:26:45

The solution for the system of equations is:
$color(blue)(x=-2, y=5$

$color(blue)(4x)+3y=7$ ............equation $(1)$

$-2x+y=9$ , multiplying this equation by $2$
$color(blue)(-4x)+2y=18$ ......equation $(2)$

Now, we can solve the system of equations through elimination.
Adding the two equations eliminates $color(blue)(4x$

$cancelcolor(blue)(4x)+3y=7$
$cancelcolor(blue)(-4x)+2y=18$

$5y=25$

$color(blue)(y=5$

Now, we find $x$ by substituting the value of $y$ in equation $1$ :

$4x+3y=7$

$4x=7-3y$

$x=(7-3y)/4$

$x=((7-3*5))/4$

$x=((7-15))/4$

$x=-8/4$

$color(blue)(x=-2$