Solve the given system by the substitution method.
3x + y = 17
5x -2y = 10
http://www.regentsprep.org/regents/math/algebra/AE3/AlgSys.htm
To solve the system of equations using the substitution method, we need to isolate one variable in one equation and substitute it into the other equation. Let's start by isolating a variable in the first equation.
1) 3x + y = 17
To isolate y in terms of x, we can subtract 3x from both sides of the equation:
y = 17 - 3x
Now that we have an expression for y in terms of x, we can substitute it into the second equation:
2) 5x - 2y = 10
Replace y with its expression from equation 1:
5x - 2(17 - 3x) = 10
Simplify the equation:
5x - 34 + 6x = 10
Combine like terms:
11x - 34 = 10
Next, we need to isolate x by getting rid of the constant term (-34). Add 34 to both sides of the equation:
11x = 10 + 34
Simplify:
11x = 44
Finally, divide both sides of the equation by 11 to solve for x:
x = 44/11
Simplify:
x = 4
Now that we've found the value of x, substitute it back into the expression for y:
y = 17 - 3x
Substitute x = 4:
y = 17 - 3(4)
Simplify:
y = 17 - 12
y = 5
Therefore, the solution to the system of equations is x = 4 and y = 5.