Solve the System
2x-8y=20
3x-12y=30
-6x + 24y =-60
6x - 24y = 60
there are infinite solution.
To solve this system of equations, we'll use the method of substitution. Here are the steps:
Step 1: Solve one equation for one variable in terms of the other variable.
In this case, we'll solve the first equation for x:
2x - 8y = 20
2x = 20 + 8y
x = 10 + 4y
Step 2: Substitute the expression for the variable you solved for in step 1 into the second equation.
Now, substitute the expression we found for x into the second equation:
3x - 12y = 30
3(10 + 4y) - 12y = 30
Step 3: Simplify and solve for y.
Distribute the 3:
30 + 12y - 12y = 30
30 = 30
This equation is true, but it doesn't provide any information about y. This means that the value of y can be any real number.
Step 4: Solve for x.
Using the expression we found for x:
x = 10 + 4y
Plug in any value of y to get the corresponding value of x.
For example, if y = 0, then:
x = 10 + 4(0)
x = 10 + 0
x = 10
So, one solution to the system is x = 10 and y = 0.
By varying the value of y, you'll get a different value for x, and each pair (x, y) will be a solution to the system of equations.