solve the system using substitution
x+3.5y=9.5
2x+2y=14
We can solve the first equation for x:
x = 9.5 - 3.5y
Substitute this expression for x in the second equation:
2(9.5 - 3.5y) + 2y = 14
Distribute and simplify:
19 - 7y + 2y = 14
Combine like terms:
19 - 5y = 14
Subtract 19 from both sides:
-5y = -5
Divide by -5 on both sides:
y = 1
Substitute this value for y in 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 of equations using substitution, we will solve one equation for one variable and then substitute that expression into the other equation.
Let's begin by solving the first equation, x + 3.5y = 9.5, for x:
x = 9.5 - 3.5y
Now we substitute this expression for x into the second equation, 2x + 2y = 14:
2(9.5 - 3.5y) + 2y = 14
Now we simplify and solve for y:
19 - 7y + 2y = 14
-5y = -5
y = 1
To find x, we substitute the value of y into the first equation:
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 the system of equations using the method of substitution, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the second equation, 2x + 2y = 14, for x:
2x = 14 - 2y
x = (14 - 2y) / 2
x = 7 - y
Step 2: Substitute the expression of the variable from Step 1 into the other equation.
Substitute x = 7 - y into the first equation:
x + 3.5y = 9.5
(7 - y) + 3.5y = 9.5
7 + 2.5y = 9.5
Step 3: Solve the resulting equation for the variable.
2.5y = 9.5 - 7
2.5y = 2.5
y = 2.5 / 2.5
y = 1
Step 4: Substitute the value of y back into one of the original equations and solve for x.
Using the second equation, 2x + 2y = 14:
2x + 2(1) = 14
2x + 2 = 14
2x = 14 - 2
2x = 12
x = 12 / 2
x = 6
Therefore, the solution to the system of equations is x = 6 and y = 1.