solve simultaneous equation by substitution method 3x+2y=12, 4x-3y=1
To solve the simultaneous equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, 3x + 2y = 12, for x:
3x = 12 - 2y
x = (12 - 2y) / 3
Step 2: Substitute the expression for the variable found in step 1 into the other equation.
Substitute x = (12 - 2y) / 3 into the second equation, 4x - 3y = 1:
4((12 - 2y) / 3) - 3y = 1
Step 3: Simplify and solve for y.
Multiply both sides of the equation by 3 to eliminate the fraction:
4(12 - 2y) - 9y = 3
48 - 8y - 9y = 3
48 - 17y = 3
-17y = 3 - 48
-17y = -45
y = (-45) / (-17)
y = 45/17
Step 4: Substitute the value of y found in step 3 into the expression for x from step 1.
Substitute y = 45/17 into x = (12 - 2y) / 3:
x = (12 - 2(45/17)) / 3
x = (12 - 90/17) / 3
x = (204/17 - 90/17) / 3
x = (114/17) / 3
x = (114/17) * (1/3)
x = 38/17
Therefore, the solution to the simultaneous equations is x = 38/17 and y = 45/17.
To solve the given system of simultaneous equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable.
Let's solve the first equation, 3x+2y=12, for x:
3x = 12 - 2y
Divide both sides by 3:
x = (12 - 2y) / 3
Step 2: Substitute the obtained expression for x into the other equation.
Substitute the expression x = (12 - 2y) / 3 into the second equation, 4x-3y=1:
4((12 - 2y) / 3) - 3y = 1
Simplify the equation:
(4/3)(12 - 2y) - 3y = 1
Multiply through by 3 to get rid of the fraction:
4(12 - 2y) - 9y = 3
Step 3: Solve the equation obtained.
Now, solve this equation to find the value of y. Distribute and combine like terms:
(48 - 8y) - 9y = 3
48 - 8y - 9y = 3
48 - 17y = 3
Subtract 48 from both sides:
-17y = 3 - 48
-17y = -45
Divide both sides by -17:
y = (-45) / (-17)
y = 45 / 17 (exact solution)
Step 4: Substitute the value of y back into one of the original equations.
Let's substitute the value of y into the first equation, 3x+2y=12:
3x + 2(45/17) = 12
3x + (90/17) = 12
Multiply through by 17 to eliminate the fraction:
17(3x) + 90 = 204
51x + 90 = 204
Subtract 90 from both sides:
51x = 204 - 90
51x = 114
Divide both sides by 51:
x = 114 / 51
x = 38 / 17 (exact solution)
Step 5: Write the final solution as an ordered pair (x, y).
The solution to the system of equations is:
x = 38 / 17
y = 45 / 17
So, the solution in the form of an ordered pair is (38/17, 45/17).
20 x, 50=y
substitution is not the ideal way for this example, but anyway.....
from 3x+2y = 12 ---> y = (12-3x)/2
sub into the 2nd:
4x - 3(12-3x)/2 = 1
multiply by 2
8x - 3(12-3x) = 2
8x - 36 + 9x = 2
17x = 38
x = 38/17
then y = (12 - 3(38/17))/2
= (12 - 114/17)/2
= 6 - 57/17 = 45/17
I would have done the following using elimination:
1st times 3 ----> 9x + 6y = 36
2nd times 2 ----> 8x - 6y = 2
add them: 17x = 38
x = 38/17
sub into 1st:
3(38/17) + 2y = 12
2y = 12 - 114/17 = 90/17
y = 45/17
The final fractional answers of course could not be avoided, but
getting there involved less fractional work.