solve using substitution:
4x+9y=24
y=1/3x+2
y = ( 1 / 3 ) x + 2
4 x + 9 y = 24
4 x + 9 [ ( 1 / 3 ) x + 2 ] = 24
4 x + ( 9 / 3 ) x + 18 = 24
4 x + 3 x + 18 = 24
7 x + 18 = 24 Subtract 18 to both sides
7 x - 18 = 24 - 18
7 x = 6 Divide both sides by 7
x = 6 / 7
y = ( 1 / 3 ) x + 2
y = ( 1 / 3 ) 6 / 7 + 2
y = 1 * 6 / ( 3 * 7 ) + 2
y = 6 / 21 + 2
y = 6 / 21 + 42 / 21
y = 48 / 21
y = 3 * 16 / ( 3 * 7 )
y = 16 / 7
You posted the same question 3 times within about 20 minutes, causing an unnecessary duplication in a solution.
Have patience.
To solve this system of equations using substitution, we will substitute the value of y from the second equation into the first equation. Here's how to do it step by step:
Step 1: Given equations
4x + 9y = 24 ...(Equation 1)
y = (1/3)x + 2 ...(Equation 2)
Step 2: Substitute Equation 2 into Equation 1
4x + 9((1/3)x + 2) = 24
Step 3: Simplify the equation
4x + (9/3)x + 18 = 24
Step 4: Combine like terms
4x + 3x + 18 = 24
7x + 18 = 24
Step 5: Move constant term to the other side
7x = 24 - 18
7x = 6
Step 6: Solve for x
x = 6/7
Step 7: Substitute the value of x into Equation 2 to find y
y = (1/3)(6/7) + 2
To simplify, multiply 1/3 and 6/7:
y = 2/7 + 2
Combine the fractions:
y = 2/7 + 14/7
y = 16/7
So, the solution to the system of equations is:
x = 6/7
y = 16/7