Please help me to solve by substitution method.
7x+8y =44
x=41-5y
7 x 41-5y+8y=44
287+3y=44
3y=-287+44
3y=-243
y=-243 divided by 3
y=81
Patty should have used brackets
in 7x + 8y = 44
7(41-5y) + 8y = 44
287 - 35y + 8y = 44
-27y = -243
y = 9
then in x= 41-5y
x = 41-45
x = -4
so x=-4 and y = 9
To solve the system of equations using the substitution method, you will need to follow these steps:
Step 1: Start with one of the equations and solve for one variable in terms of the other variable.
Let's start with the second equation:
x = 41 - 5y
Step 2: Substitute the expression you found for one variable into the other equation.
Now, we will substitute x in the first equation with 41 - 5y:
7(41 - 5y) + 8y = 44
Step 3: Simplify and solve the resulting equation.
Distribute the 7:
287 - 35y + 8y = 44
Combine like terms:
-27y + 287 = 44
Step 4: Isolate the variable y.
Subtract 287 from both sides:
-27y = -243
Divide both sides by -27 to solve for y:
y = 9
Step 5: Substitute the value of y back into one of the original equations to solve for x.
Let's use the second equation:
x = 41 - 5y
x = 41 - 5(9)
x = 41 - 45
x = -4
Step 6: Check the solution by substituting the values of x and y into both original equations.
Substituting into the first equation:
7x + 8y = 44
7(-4) + 8(9) = 44
-28 + 72 = 44
44 = 44 (True)
Substituting into the second equation:
x = 41 - 5y
-4 = 41 - 5(9)
-4 = 41 - 45
-4 = -4 (True)
Therefore, the solution to the system of equations is x = -4 and y = 9.