how do i solve x+3y=56
There is an infinite number of solutions to x+3y=56.
Do you particularly favor any one solution?
Since this is a single equation containing two unknowns (x and y), it is not possible to have an explicit solution for x and y.
The given equation expresses the relationship between x and y, namely if one is known , we can find the value of the other.
The relationship can also be expressed as a straight line graph, or by expressing the equation differently:
x+3y=56, or
x=56-3y, or
y=(56-x)/3
The set of possible solution to the equation is called the solution set, which might contain:
{(2,18), (5,17), (8,16), ...}
To solve the equation x + 3y = 56, you can use either the substitution method or the elimination method. I will explain the elimination method here:
Step 1: Manipulate the equation to eliminate one variable. In this case, let's eliminate the variable x by multiplying the entire equation by -1. This gives us -x - 3y = -56.
Step 2: Add the two equations together to eliminate x. The -x and x terms will cancel out since they are additive inverses. The resulting equation is -4y = -112.
Step 3: Solve for y by dividing both sides of the equation by -4. This gives us y = 28.
Step 4: Substitute the value of y back into one of the original equations. Let's use x + 3y = 56. Plugging in y = 28, we have x + 3 * 28 = 56.
Step 5: Simplify the equation by performing the multiplication. This gives us x + 84 = 56.
Step 6: Solve for x by subtracting 84 from both sides of the equation. This gives us x = -28.
So, the solution to the equation x + 3y = 56 is x = -28 and y = 28.