solve by the substitution method 7x+4y=14, x=47-7y please help
To solve the given system of equations using the substitution method, follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
In this case, we have x = 47 - 7y from the second equation.
Step 2: Substitute the expression obtained in step 1 into the other equation.
Now, substitute x = 47 - 7y into the first equation:
7(47 - 7y) + 4y = 14
Step 3: Simplify and solve the resulting equation.
Expand and simplify the equation:
329 - 49y + 4y = 14
Combine like terms:
-45y = -315
Divide both sides by -45:
y = -315 / -45
y = 7
Step 4: Substitute the value of y obtained in step 3 back into one of the original equations to find the value of the other variable.
Using the first equation:
7x + 4y = 14
Replace y with 7:
7x + 4(7) = 14
7x + 28 = 14
Subtract 28 from both sides:
7x = -14
Divide both sides by 7:
x = -14 / 7
x = -2
Therefore, the solution to the system of equations is x = -2 and y = 7.