Question

Determine which answer choice matches the graph you drew and identify the solution to the system.

Answer 1

Given:

The system of linear equation is given as,

$\begin{gathered} y\text{ = 2x + 1 \_\_\_\_\_\_\_\_\_\lparen1\rparen} \\ y\text{ = -x + 4\_\_\_\_\_\_\_\_\_\lparen2\rparen} \end{gathered}$

Required:

The solution to the system of linear equation.

Explanation:

Substituting the equation (2) in equation (1),

$\begin{gathered} -x\text{ + 4 = 2x + 1} \\ \end{gathered}$

Rearranging the like terms on both the sides,

$\begin{gathered} 2x\text{ + x = 4 - 1 } \\ 3x\text{ = 3} \\ x\text{ = 1} \end{gathered}$

Substituting the value of x = 1 in equation ( 1 ),

$\begin{gathered} y\text{ = 2x + 1} \\ y\text{ = 2\lparen1\rparen + 1 } \\ y\text{ = 2 + 1} \\ y\text{ = 3} \end{gathered}$

(1, 3) is the point where the line representing both the equations intersects on the graph.

Answer:

Thus the solution set is ( 1 , 3 ).