Question

Solve the system of equations using substitution.

Given: (begin{cases} 3x - y = 5 2x + y = 7 end{cases})
a) (x = 2, y = 1)
b) (x = 1, y = 2)
c) (x = 3, y = 4)
d) (x = 4, y = 3)

Answer 1

To solve the given system of equations using substitution, isolate one variable in one equation, substitute it into the other equation, solve for the remaining variable, substitute back into the original equations, and verify the solution. In this case, the solution is (x = 2, y = 1).

Step-by-step explanation:

To solve the given system of equations using substitution:

1. Isolate one variable in one equation, preferably the variable with a coefficient of 1.
2. Substitute the isolated variable into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value of the remaining variable back into one of the original equations to find the value of the isolated variable.
5. Verify the solution by substituting the values of both variables into the other equation.

In this case, we can isolate y in the first equation by rearranging it as y = 3x - 5. We can then substitute this expression for y in the second equation, resulting in 2x + (3x - 5) = 7. Solving this equation yields x = 2. Substituting x = 2 into the first equation gives y = 1.

Therefore, the solution to the system of equations is (x = 2, y = 1), which corresponds to option a).