+655 Find $a+b+c$, given that $x+y\neq -1$ and \begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y,\\ ay+b+cx&=4x+y. \end{align*}
+9481 Find \(a+b+c\) , given that \(x+y\neq -1\) and \( \begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y,\\ ay+b+cx&=4x+y. \end{align*}\)
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(ax + by + c) + (a + bx + cy) + (ay + b + cx) = (ax + by + c) + (a + bx + cy) + (ay + b + cx)
(ax + by + c) + (a + bx + cy) + (ay + b + cx) = (x + 7) + (2x + 6y) + (4x + y)
ax + by + c + a + bx + cy + ay + b + cx = x + 7 + 2x + 6y + 4x + y
ax + bx + cx + ay + by + cy + a + b + c = 7x + 7y + 7
x(a + b + c) + y(a + b + c) + 1(a + b + c) = 7(x + y + 1)
(a + b + c)(x + y + 1) = 7( x + y + 1)
a + b + c = 7
+9481 Find \(a+b+c\) , given that \(x+y\neq -1\) and \( \begin{align*} ax+by+c&=x+7,\\ a+bx+cy&=2x+6y,\\ ay+b+cx&=4x+y. \end{align*}\)
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(ax + by + c) + (a + bx + cy) + (ay + b + cx) = (ax + by + c) + (a + bx + cy) + (ay + b + cx)
(ax + by + c) + (a + bx + cy) + (ay + b + cx) = (x + 7) + (2x + 6y) + (4x + y)
ax + by + c + a + bx + cy + ay + b + cx = x + 7 + 2x + 6y + 4x + y
ax + bx + cx + ay + by + cy + a + b + c = 7x + 7y + 7
x(a + b + c) + y(a + b + c) + 1(a + b + c) = 7(x + y + 1)
(a + b + c)(x + y + 1) = 7( x + y + 1)
a + b + c = 7
