solve by substitution method
9x+7y=-23
x=48-8y
Substitute 48 - 8y for x in the first equation and solve for y. Put that value in the second equation to find x. Check by putting both values in the first equation.
To solve the given system of equations using the substitution method, follow these steps:
Step 1: Start with one equation and solve it for one variable in terms of the other variable.
Given equations:
1) 9x + 7y = -23
2) x = 48 - 8y
In equation (2), x is already isolated, so no further simplification is required.
Step 2: Substitute the expression obtained for that variable from step 1 into the other equation.
We substitute x = 48 - 8y from equation (2) into equation (1) as follows:
9(48 - 8y) + 7y = -23
Step 3: Simplify and solve the resulting equation for the remaining variable.
Expanding the equation, we get:
432 - 72y + 7y = -23
Combine like terms:
-65y + 432 = -23
Step 4: Solve for y by isolating the variable.
Subtract 432 from both sides:
-65y = -23 - 432
-65y = -455
Divide both sides by -65:
y = (-455) / (-65)
y = 7
Step 5: Substitute the value of y back into equation (2) to find the value of x.
Using equation (2):
x = 48 - 8y
x = 48 - 8(7)
x = 48 - 56
x = -8
Therefore, the solution of the system of equations is x = -8 and y = 7.