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Question

Question: How do you solve for \(y\) in \(- 3x + 5y = - 10\) ?...

How do you solve for yy in 3x+5y=10- 3x + 5y = - 10 ?

Explanation

Solution

The equation that we need to solve here is a linear equation in two variables. But we need to solve this equation only for one variable. For that, we will simplify it by the way that we will keep the required variable terms on the left and the remaining terms on right and then simplify it further.

Complete step by step answer:
The given equation 3x+5y=10- 3x + 5y = - 10 , is a linear equation in two variables.
Here, we need to solve this equation for one variable only. So we simplify it further.
To solve it for yy , we add 3  x3\;x on both sides, then we get
3x+5y+3x=10+3x- 3x + 5y + 3x = - 10 + 3x
Because we know that positive and negative of the same term becomes zero.
5y=10+3x\Rightarrow 5y = - 10 + 3x ,
Now, to make the coefficient of yy , 11 , we divide the above equation by 55 on both sides,
5y5=10+3x5\Rightarrow \dfrac{{5y}}{5} = \dfrac{{ - 10 + 3x}}{5}
y=105+3x5\Rightarrow y = \dfrac{{ - 10}}{5} + \dfrac{{3x}}{5} ,
Now the coefficient of yy becomes 11 ,
y=2+3x5\Rightarrow y = - 2 + \dfrac{{3x}}{5} ,
y=3x52\Rightarrow y = \dfrac{{3x}}{5} - 2 ,
This equation can also be written like this, as the commutative property for addition holds.

Hence, y=3x52y = \dfrac{{3x}}{5} - 2 is the required solution of the given equation for yy .

Additional information:
The linear equation means that the degree of the equation is 11 . In other words, we say that the highest power of the variables in the equation is 11 . Thus we say that this is a linear equation. A linear equation represents a line.

Note: The representation of a linear equation in two variables is not unique. As y=3x52y = \dfrac{{3x}}{5} - 2 , can be written as y=2+3x5y = - 2 + \dfrac{{3x}}{5} . Also, any pair of values of variables satisfying a given linear equation is known as its solution.