Solve the system by substitution.
y, equals, 8, x, plus, 6
y=
8x+6
10, x, minus, 5, y, equals, 30
10x−5y=
30
To solve the system by substitution, we need to solve one equation for one variable and substitute that expression into the other equation.
Let's solve the first equation, y = 8x + 6, for y:
y = 8x + 6
Now, substitute this expression for y into the second equation:
10x - 5(8x + 6) = 30
Simplifying the equation:
10x - 40x - 30 = 30
-30x - 30 = 30
Adding 30 to both sides:
-30x - 30 + 30 = 30 + 30
-30x = 60
Dividing both sides by -30:
-30x/-30 = 60/-30
x = -2
Now that we have found the value of x, we can substitute it back into the first equation to find y:
y = 8(-2) + 6
y = -16 + 6
y = -10
Thus, the solution to the system of equations is x = -2 and y = -10.