For this case we have the following equation:
[tex]7c + 7a-7r + 8m + 2y = 31[/tex]
We solve for c:
We pass the terms that do not contain "c" to the other side of the equation by changing signs:
[tex]7c = 31-7a + 7r-8m-2y[/tex]
We divide by 7 on both sides of the equation:
[tex]c = \frac {31-7a + 7r-8m-2y} {7}[/tex]
We solve for "a":
We pass the terms that do not contain "a" to the other side of the equation by changing signs:
[tex]7a = 31-7c + 7r-8m-2y[/tex]
We divide by 7 on both sides of the equation:
[tex]a = \frac {31-7c + 7r-8m-2y} {7}[/tex]
We solve for r:
We pass the terms that do not contain "r" to the other side of the equation by changing signs:
[tex]-7r = 31-7c-7a-8m-2y[/tex]
We multiply by -1 on both sides:
[tex]7r = 7c + 7a + 8m + 2y-31[/tex]
We divide by 7 on both sides of the equation:
[tex]r = \frac {7c + 7a + 8m + 2y-31} {7}[/tex]
We solve for m:
We pass the terms that do not contain "m" to the other side of the equation by changing signs:
[tex]7c + 7a-7r + 8m + 2y = 31\\8m = 31-7c-7a + 7r-2y[/tex]
We divide by 7 on both sides of the equation:
[tex]m = \frac {31-7c-7a + 7r-2y} {8}[/tex]
We solve for y:
We pass the terms that do not contain "y" to the other side of the equation by changing signs:
[tex]2y=31-7c-7a+7r-8m[/tex]
We divide by 2 on both sides of the equation:
[tex]y=\frac{31-7c-7a+7r-8m}{2}[/tex]
Answer:
[tex]c = \frac {31-7a + 7r-8m-2y} {7}[/tex]
[tex]a = \frac {31-7c + 7r-8m-2y} {7}[/tex]
[tex]r = \frac {7c + 7a + 8m + 2y-31} {7}[/tex]
[tex]m = \frac {31-7c-7a + 7r-2y} {8}[/tex]
[tex]y=\frac{31-7c-7a+7r-8m}{2}[/tex]
