Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. Solve the system by substitution. x+3.5y=9.5 2x+2y=14
To solve the system by substitution, we will first solve one of the equations for one variable and then substitute it into the other equation.
Let's solve the first equation, x + 3.5y = 9.5, for x:
x = 9.5 - 3.5y
Now we will substitute this value of x into the second equation, 2x + 2y = 14:
2(9.5 - 3.5y) + 2y = 14
Distribute the 2:
19 - 7y + 2y = 14
Combine like terms:
-5y + 19 = 14
Subtract 19 from both sides:
-5y = 14 - 19
-5y = -5
Divide by -5:
y = -5/-5
y = 1
Now substitute this value of y back into the first equation to find x:
x + 3.5(1) = 9.5
x + 3.5 = 9.5
x = 9.5 - 3.5
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 1.
To solve this system of equations by substitution, we'll first solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation for x:
x + 3.5y = 9.5
Rearranging the equation, we get:
x = 9.5 - 3.5y
Now we can substitute this expression for x into the second equation:
2x + 2y = 14
Substituting x = 9.5 - 3.5y, we have:
2(9.5 - 3.5y) + 2y = 14
Expanding the expression, we get:
19 - 7y + 2y = 14
Combining like terms, we have:
19 - 5y = 14
Next, we'll isolate the variable y. Subtracting 19 from both sides gives us:
-5y = 14 - 19
-5y = -5
Dividing both sides by -5, we find:
y = -5 / -5
y = 1
Now that we know y, we can substitute this value back into either of the original equations to find x. Let's use the first equation:
x + 3.5y = 9.5
Substituting y = 1, we have:
x + 3.5(1) = 9.5
x + 3.5 = 9.5
Subtracting 3.5 from both sides, we have:
x = 9.5 - 3.5
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 1.
To solve the given system of equations using the method of substitution, we need to solve one equation for one variable and then substitute that expression into the other equation.
Let's solve the first equation, x + 3.5y = 9.5, for x:
x = 9.5 - 3.5y (equation 1)
Now, substitute this expression for x in the second equation, 2x + 2y = 14:
2(9.5 - 3.5y) + 2y = 14 (substituting x into the equation)
Now, simplify and solve for y:
19 - 7y + 2y = 14
Combine like terms:
19 - 5y = 14
Subtract 19 from both sides:
-5y = 14 - 19
-5y = -5
Divide by -5:
y = 1
Now that we have the value of y, substitute it back into equation 1 to find 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.