11x-8y=-48
The equation is in standard form for a linear equation, which is Ax + By = C.
To rewrite the equation in slope-intercept form, which is y = mx + b, we need to isolate y.
11x - 8y = -48
-8y = -11x - 48
y = (11/8)x + 6
Therefore, the equation in slope-intercept form is y = (11/8)x + 6.
To solve the equation 11x - 8y = -48, we can use the method of isolating one variable and solving for the other. Let's solve for x.
Step 1: Move the term containing y to the other side of the equation.
11x - 8y = -48
11x = 8y - 48
Step 2: Divide both sides of the equation by 11 to isolate x.
x = (8y - 48)/11
So, the equation 11x - 8y = -48 can be rewritten as x = (8y - 48)/11.
To find the values of x and y that satisfy the equation 11x - 8y = -48, you can use various methods such as substitution or elimination.
1. Substitution Method:
Step 1: Solve one of the equations for either x or y.
Let's solve the equation for x:
11x - 8y = -48
11x = 8y - 48
x = (8y - 48)/11
Step 2: Substitute the value of x from the solved equation into the other equation.
We have only one equation, so we'll use the original equation:
11x - 8y = -48
11((8y - 48)/11) - 8y = -48
8y - 48 - 8y = -48
-48 = -48
This equation is true for all values of y. Therefore, there are infinitely many solutions to this equation, and any combination of x and y that satisfies the equation will be a solution.
2. Elimination Method:
Step 1: Multiply both sides of the equation by a constant to make the coefficients of x and y equal to each other.
In this case, we can multiply the equation by 8 so that the coefficients of x and y are the same.
8(11x - 8y) = 8(-48)
88x - 64y = -384
Step 2: Distribute and simplify.
88x - 64y = -384
Step 3: Rearrange the equation in the form Ax + By = C.
88x - 64y + 384 = 0
Now we have the equation in a standard form. The values of x and y that satisfy this equation will be the solutions.
In this case, there are infinitely many solutions to this equation.