Question

Solve, using the substitution method.

x + y = 5

x – y = 3

Question 1 options:

There is no solution.


The solution is (2, –1)

The solution is (4, 1)

There are an infinite number of solutions.

Answer 1

Explanation:

To solve the system of equations using the substitution method, we need to solve one of the equations for one of the variables, and then substitute that expression into the other equation.

Let's solve the first equation, x + y = 5, for y:

y = 5 - x

Now, substitute this expression for y in the second equation, x - y = 3:

x - (5 - x) = 3

Simplifying the left side of the equation:

2x - 5 = 3

Adding 5 to both sides:

2x = 8

Dividing both sides by 2:

x = 4

Now that we know x = 4, we can substitute this value back into either of the original equations to find y. Let's use the first equation:

x + y = 5

4 + y = 5

y = 1

Therefore, the solution to the system of equations is (4, 1).

So, the correct option is: The solution is (4, 1).