How do you do the equation 8x+20y=10 solve for y and x
To solve the equation 8x + 20y = 10 for y and x, we'll use a method called "substitution." Here is the step-by-step process:
Step 1: Solve for y:
Rearrange the equation to isolate the term containing y.
20y = 10 - 8x
Step 2: Divide both sides of the equation by 20 to solve for y:
(20y) / 20 = (10 - 8x) / 20
y = (10 - 8x) / 20
Step 3: Simplify the equation further, if possible:
Distribute the division:
y = 10/20 - (8x / 20)
y = 1/2 - 2x / 5
So, the equation is now y = 1/2 - 2x / 5.
Step 4: Solve for x:
There are infinite solutions for x, so we'll express x in terms of a parameter, let's say t.
x = t
Step 5: Substitute the value of x into the equation to solve for y:
y = 1/2 - 2(t) / 5
y = 1/2 - 2t / 5
Therefore, the solutions for the equation 8x + 20y = 10, in terms of x and y, are:
x = t
y = 1/2 - 2t / 5
To solve the given equation 8x + 20y = 10 for y and x, we can use the method of substitution or elimination. Let's use the method of substitution in this case.
Step 1: Solve for y
To isolate y, we'll rearrange the equation as follows:
20y = 10 - 8x
Step 2: Simplify the equation
Divide both sides of the equation by 20 to solve for y:
y = (10 - 8x) / 20
Step 3: Simplify further if possible
The equation y = (10 - 8x) / 20 can be simplified by factoring out the common factor:
y = (1 - (4/5)x)
Hence, the equation 8x + 20y = 10 can be solved for y as y = (1 - (4/5)x).
Now, we can solve for x.
Step 1: Solve for x
To isolate x, we'll rearrange the equation as follows:
8x = 10 - 20y
Step 2: Simplify the equation
Divide both sides of the equation by 8 to solve for x:
x = (10 - 20y) / 8
Step 3: Simplify further if possible
The equation x = (10 - 20y) / 8 can be simplified by dividing each term by 2:
x = (5 - 10y) / 4
Thus, the equation 8x + 20y = 10 can be solved for x as x = (5 - 10y) / 4.