How do you solve the following system: $7 x - 5 y = - 11, 7 x - y = 10$ $7x − 5y = −11, 7x - y = 10$ ?

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Answer 1 · 2016-01-03T18:21:41

$x = \frac{61}{28}, y = \frac{21}{4}$ $color(blue)(x=61/28, y=21/4$

$7 x - 5 y = - 11$ $color(blue)(7x)-5y=-11$ ....equation $1$ $1$

$7 x - y = 10$ $color(blue)(7x)-y=10$ .....equation $2$ $2$

Solving by elimination

Subtracting equation $2$ $2$ from $1$ $1$ :

$cancelcolor(blue)(7x)-5y=-11$

$-cancelcolor(blue)(7x)+y=-10$

$-4y=-21$

$y=(-21)/(-4)$

$color(blue)(y=21/4$

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

$7x-5y=-11$

$7x=-11+5y$

$7x=-11+5xx(21/4)$

$7x=-11+(105/4)$

$7x=-44/4+(105/4)$

$7x=61/4$

$color(blue)(x=61/28$

The solution for the system of equations is :

$color(blue)(x=61/28, y=21/4$

How do you solve the following system: 7x − 5y = −11, 7x - y = 10 7x−5y=−11,7x−y=10 7x − 5y = −11, 7x - y = 10 ?