how do you solve 9x+8y=11 for x and y
You need two independent equations to get unique values for x and y.
the problem asks if (1,-6) is a solution to this equation and this is all it gives me
Well that is a help!
(1,-6)
and
9x+8y=11 for x and y
well now
9(1) +8(-6) = 11 ? or not?
9 - 48 = 11 ? NO WAY
To solve the equation 9x + 8y = 11 for x and y, we will use a method called "solving by substitution." This method involves isolating one variable in terms of the other and then substituting that expression back into the original equation to find the value of the other variable.
Step 1: Solve for x in terms of y
Start by isolating x in terms of y in the equation 9x + 8y = 11. To do this, subtract 8y from both sides:
9x + 8y - 8y = 11 - 8y
9x = 11 - 8y
Step 2: Solve for x
We want to solve for x, so divide both sides of the equation by 9:
9x/9 = (11 - 8y)/9
x = (11 - 8y)/9
Now we have x expressed in terms of y.
Step 3: Substitute the value of x back into the original equation
Take the expression we found for x [(11 - 8y)/9] and substitute it back into the original equation 9x + 8y = 11:
9((11 - 8y)/9) + 8y = 11
Step 4: Simplify the equation
Simplify the equation by canceling out common factors and distributing:
11 - 8y + 8y = 11
The -8y and +8y cancel each other out, leaving us with:
11 = 11
Step 5: Analyze the result
The final equation 11 = 11 is always true, which means there are an infinite number of solutions to this system of equations. In other words, any values of x and y that satisfy the original equation, 9x + 8y = 11, will be a valid solution to this system.