Solve by substitution
2x+3y=40.50
3x+y=38.00
Use the process of elimation and elimate the x varible. This gives you the y variable. Then you substitue this answer for the x varible. If you need any help with the process of elimantion, I could asist you more.
However, using substitution,
pick either equation and solve for a variable:
3x+y = 38.0
so,
y = 38-3x
Now substitute that value into the other equation:
2x+3y=40.50
2x + 3(38-3x) = 40.5
2x + 114 - 9x = 40.5
-7x = -73.5
x = 10.5
y = 38-3x = 6.5
To solve the system of equations by substitution, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for y:
3x + y = 38
y = 38 - 3x
Step 2: Substitute the expression of the variable found in step 1 into the other equation.
Now, substitute the expression for y in the first equation:
2x + 3(38 - 3x) = 40.50
Step 3: Simplify and solve for x.
Distribute 3 to the terms inside the parenthesis:
2x + 114 - 9x = 40.50
Combine like terms:
-7x + 114 = 40.50
Subtract 114 from both sides:
-7x = -73.50
Divide both sides by -7 to isolate x:
x = -73.50 ÷ -7 = 10.50
Step 4: Substitute the value of x back into one of the equations to solve for y.
Let's use the second equation:
3(10.50) + y = 38
Multiply 3 by 10.50:
31.50 + y = 38
Subtract 31.50 from both sides:
y = 38 - 31.50 = 6.50
Step 5: Check the solution.
Substitute the values of x and y back into both original equations to verify if the solution is valid.
Using the first equation:
2(10.50) + 3(6.50) = 40.50
21 + 19.50 = 40.50
40.50 = 40.50
Using the second equation:
3(10.50) + 6.50 = 38
31.50 + 6.50 = 38
38 = 38
Since both equations are satisfied, the solution is x = 10.50 and y = 6.50.