Solve the given system by the substitution method.
3x + y = 17
5x -2y = 10
solve for y in the first equation, put that value for y into the second equation.
I will be happy to check your work.
To solve the given system of equations using the substitution method, we will solve one equation for one variable and substitute that expression into the other equation.
Let's solve the first equation, 3x + y = 17, for y:
1. Start by isolating y.
Subtract 3x from both sides of the equation:
y = 17 - 3x
Now, substitute this expression for y in the second equation, 5x - 2y = 10:
2. Replace y with (17 - 3x):
5x - 2(17 - 3x) = 10
Now, solve this equation for x:
3. Distribute -2 to both terms inside the parentheses:
5x - 34 + 6x = 10
4. Combine like terms:
11x - 34 = 10
5. Add 34 to both sides of the equation:
11x = 44
6. Divide both sides by 11 to solve for x:
x = 4
Now that we have found the value of x, substitute it back into the first equation to solve for y:
7. Replace x with 4 in 3x + y = 17:
3(4) + y = 17
12 + y = 17
8. Subtract 12 from both sides of the equation:
y = 17 - 12
y = 5
Therefore, the solution to the given system of equations is x = 4 and y = 5.