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Solve the system by substitution.
x+3.5y=9.5
2x+2y=14
We can solve the first equation for x:
x = 9.5 - 3.5y
Now, we substitute this expression for x in the second equation:
2(9.5 - 3.5y) + 2y = 14
Distribute 2:
19 - 7y + 2y = 14
Combine like terms:
-5y + 19 = 14
Subtract 19 from both sides:
-5y = -5
Divide both sides by -5:
y = 1
Now, we can substitute this value of y back into the first equation:
x + 3.5(1) = 9.5
x + 3.5 = 9.5
Subtract 3.5 from both sides:
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 1.
To solve the system by substitution, we will solve one equation for one variable and substitute that expression into the other equation.
Let's solve the first equation for x:
x + 3.5y = 9.5
Subtract 3.5y from both sides:
x = 9.5 - 3.5y
Now substitute this expression for x in the second equation:
2x + 2y = 14
Replace x with 9.5 - 3.5y:
2(9.5 - 3.5y) + 2y = 14
Distribute 2 to the terms inside the parentheses:
19 - 7y + 2y = 14
Combine like terms:
-5y + 19 = 14
Subtract 19 from both sides:
-5y = 14 - 19
-5y = -5
Divide both sides by -5:
y = -5 / -5
y = 1
Now that we have the value of y, we can substitute it back into the first equation to find x:
x + 3.5(1) = 9.5
x + 3.5 = 9.5
Subtract 3.5 from both sides:
x = 9.5 - 3.5
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 1.
To solve the system of equations by substitution, we'll start by solving one of the equations for one variable and then substitute the expression into the other equation.
Let's solve the first equation, x + 3.5y = 9.5, for x:
x = 9.5 - 3.5y
Now we'll substitute this expression for x into the second equation, 2x + 2y = 14:
2(9.5 - 3.5y) + 2y = 14
Simplify the equation:
19 - 7y + 2y = 14
Combine like terms:
19 - 5y = 14
Next, we'll isolate the variable y. Subtract 19 from both sides of the equation:
-5y = 14 - 19
-5y = -5
Now divide both sides of the equation by -5:
y = -5 / -5
y = 1
We have found the value of y, which is 1. Now we can substitute this value back into the first equation to solve for x:
x = 9.5 - 3.5(1)
x = 9.5 - 3.5
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 1.