Solve by the substitution method.
2x + 4y = 8
-5x + y = 13
What is the solution of the system?
the 2nd equation says that y = 5x+13
So substitute that in the 1st equation, and you have
2x + 4(5x+13) = 8
Solve that for x, and then use that to get y.
To solve the system of equations by the substitution method, we need to solve one equation for one variable in terms of the other variable, and then substitute this expression into the other equation.
Let's solve the second equation for y:
-5x + y = 13
y = 5x + 13
Now we substitute this expression for y into the first equation:
2x + 4(5x + 13) = 8
Simplify the equation:
2x + 20x + 52 = 8
22x + 52 = 8
Subtract 52 from both sides:
22x = -44
Divide both sides by 22:
x = -2
Now substitute the value of x back into the equation we derived for y:
y = 5x + 13
y = 5(-2) + 13
y = -10 + 13
y = 3
Therefore, the solution of the system is x = -2 and y = 3.