4y+5x=8
The given equation is 4y + 5x = 8.
To find the solution to this equation, you can use different methods like graphing, substitution, or elimination. Let's solve it using the substitution method:
Step 1: Solve one variable in terms of the other.
Solve the equation for y in terms of x:
4y = 8 - 5x
Divide both sides by 4:
y = (8 - 5x)/4
Step 2: Substitute the expression found in Step 1 into the original equation.
Replace y in the equation 4y + 5x = 8 with (8 - 5x)/4:
4((8 - 5x)/4) + 5x = 8
Simplify the expression:
8 - 5x + 5x = 8
The x terms cancel out, leaving:
8 = 8
Step 3: Analyze the result.
In this case, the equation 8 = 8 is always true. This means that the original equation 4y + 5x = 8 is satisfied for all values of x and y.
Therefore, the solution to the equation 4y + 5x = 8 is all real numbers, as there are infinitely many solutions.