solve by subsitution
2x+y=9
8x+4y=36
8x+4y=36
4y=36-8x/4
y=9-8x
2x+y=9
2x+9-8x=9
6x=9-9
x=0
8x+4y=36
8(0)+4y=36
4y=36/4
y=9
(0,9)
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation for y:
2x + y = 9
Subtract 2x from both sides:
y = 9 - 2x
Step 2: Substitute the expression for y into the other equation.
8x + 4y = 36
Substitute y with 9 - 2x:
8x + 4(9 - 2x) = 36
Step 3: Simplify and solve for x.
Distribute the 4 into the parentheses:
8x + 36 - 8x = 36
Combine like terms:
36 = 36
The equation simplifies to 36 = 36, which is a true statement. This means that the system of equations is dependent and has infinitely many solutions.
Step 4: Solve for y.
Since the system is dependent, we can use either of the original equations to find the value of y. Let's use the first equation:
2x + y = 9
Substitute x with any value. Let's choose x = 0:
2(0) + y = 9
y = 9
So, the solution to the system of equations is x = 0 and y = 9.
To solve the system of equations using substitution, we will isolate one variable in one equation and substitute it into the other equation.
Let's start solving the system of equations:
1. Solve the first equation for x in terms of y:
2x + y = 9
Subtract y from both sides:
2x = 9 - y
Divide both sides by 2:
x = (9 - y) / 2
2. Substitute the expression for x into the second equation:
8x + 4y = 36
Replace x with (9 - y) / 2:
8((9 - y) / 2) + 4y = 36
Simplify the expression:
4(9 - y) + 4y = 36
Distribute the 4:
36 - 4y + 4y = 36
Combine like terms:
36 = 36
The equation 36 = 36 is always true, which means the system of equations is dependent and has infinite solutions. Any value of y will satisfy these equations.
To find the value of x, substitute the value of y back into either of the original equations. For example, let's use the first equation:
2x + y = 9
If we substitute y with a number, let's say 5, we get:
2x + 5 = 9
Solve for x:
2x = 9 - 5
2x = 4
x = 2
Therefore, for any value of y, the corresponding value of x that satisfies the system of equations is x = 2.