Question

Solve Systems of Linear Equations by Substitution, Identify the Nature of Solution:

2x + y = 8
y = x - 7
A. The solution is (-5,7). Infinite solutions
B. The solution is (3,-5). One solution
C. The solution is (5,3). One Solution
D. The solution is (7,-5). Infinite solutions

Answer 1

By substituting Equation 2 into Equation 1, the system of linear equations is solved to find x = 5 and y = -2. Thus, the solution of the system is (5, -2).

Step-by-step explanation:

To solve the system of linear equations by substitution, take one of the equations and solve for one variable in terms of the other. In this problem:

• 2x + y = 8 (Equation 1)
• y = x - 7 (Equation 2)

We can use Equation 2 directly to substitute for y in Equation 1.

Substituting y from Equation 2 into Equation 1 gives:

2x + (x - 7) = 8

3x - 7 = 8

Now, add 7 to both sides:

3x = 15

Divide by 3 to find x:

x = 5

Now, substitute x into Equation 2 to find y:

y = 5 - 7

y = -2

The solution of the system is (5, -2).