solve using substitution:
4x+9y=24
y=1/3x+2
sub the 2nd into the 1st
4x + 9((1/3)x+2) = 24
4x + 3x + 18 = 24
7x = 6
x = 6/7
then y = (1/3)(6/7) + 2 = 16/7
x = 6/7 , y = 16/7
To solve the system of equations using substitution, we can substitute the value of "y" from the second equation into the first equation.
Given:
4x + 9y = 24
y = (1/3)x + 2
Substitute the value of y into the first equation:
4x + 9(1/3)x + 9(2) = 24
Simplify the equation by distributing:
4x + 3x + 18 = 24
Combine like terms:
7x + 18 = 24
To isolate x, subtract 18 from both sides:
7x = 6
Divide both sides by 7:
x = 6/7
Now substitute the value of x back into the second equation to solve for y:
y = (1/3)(6/7) + 2
Simplify:
y = 2/7 + 2
To add fractions, find a common denominator:
y = 2/7 + 14/7
Combine the fractions:
y = 16/7
The solution to the system of equations is x = 6/7 and y = 16/7.
To solve the system of equations using substitution, we need to substitute the value of y from one equation into the other equation. Let's start by substituting y=1/3x+2 into the first equation.
Substitute y=1/3x+2 into the first equation:
4x + 9(1/3x+2) = 24
Now, simplify the equation by distributing the 9 into the parentheses:
4x + (9/3)x + 18 = 24
Next, simplify further by combining like terms:
4x + 3x + 18 = 24
7x + 18 = 24
To isolate x, we subtract 18 from both sides of the equation:
7x = 24 - 18
7x = 6
Lastly, divide both sides of the equation by 7 to solve for x:
x = 6/7
Now that we have found the value of x, we can substitute it back into the second equation to find the value of y.
Substitute x = 6/7 into the equation y=1/3x+2:
y = 1/3(6/7) + 2
y = 2/7 + 2
y = 2/7 + 14/7
y = 16/7
Therefore, the solution to the system of equations is x = 6/7 and y = 16/7.