Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.
x + 10y = 41
x + 9y = 37
x + 10y = 41 ... (1)
x + 9y = 37 ... (2)
For substitution, rewrite as
x = 41-10y ...(1a)
and substitute x in (2) to get
(41-10y) + 9y = 37
Simplify and solve for y.
Substitute y back in (1a) to find x.
Post for an answer check if you wish.
To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Let's solve the second equation for x in terms of y:
x + 9y = 37
x = 37 - 9y
Step 2: Substitute the expression found in step 1 into the other equation.
Substitute the expression for x from step 1 into the first equation:
x + 10y = 41
(37 - 9y) + 10y = 41
Simplify the equation:
37 - 9y + 10y = 41
37 + y = 41
Step 3: Solve for y.
Subtract 37 from both sides of the equation:
y = 41 - 37
y = 4
Step 4: Substitute the value of the found variable back into one of the original equations to solve for the other variable.
Substitute y = 4 into the first equation:
x + 10y = 41
x + 10(4) = 41
x + 40 = 41
Subtract 40 from both sides of the equation:
x = 41 - 40
x = 1
Step 5: Check the solution.
Substitute the values of x and y into the second equation to check:
x + 9y = 37
1 + 9(4) = 37
1 + 36 = 37
Both sides of the equation are equal, so the solution (x = 1, y = 4) is correct.
Therefore, the system has a unique solution: x = 1 and y = 4.