We are given the following system of equations:
3 x + 5 y = 8
y = x + 8
So we can use the "substitution method" to solve it, since the second equation is already giving us a possible substitution to make:
Replace y with x + 8 in the other equation.
We proceed as shown below:
3 x + 5 y = 8
3 x + 5 (x + 8) = 8
Use distributivr property to remove the parenthesis:
3 x + 5 x + 40 = 8
8 x + 40 = 8
subtract 40 from both sides to isolate the term in "x"
8 x = 8 - 40
8 x = - 32
divide both sides by 8 to isolate "x"
x = - 32 / 8
x = - 4
We found the requested x value
We are also asked to find y , so we use the value for x in the substitution equation:
y = x + 8
y = -4 + 8 = 4
Then y = 4
The pair that satisfies this system is x = -4 and y = 4 or in pair form: (-4, 4)
