Question

Solve the following systems by graphing. 1. x + 2y = 4 2x -y = 3

Answer 1

Given:

The system of linear equations are $x+2y=4$ and $2x-y=3$

We need to determine the solution to the system of equations by graphing.

Graphing the equation $x+2y=4$:

To graph the equation $x+2y=4$, let us determine the x and y intercepts.

x - intercept: When y = 0, then $x+2(0)=4 \implies x=4$

y - intercept: When x = 0, then $0+2y=4 \implies y=2$

The coordinates are (4,0) and (0,2)

Thus, the joining the coordinates of x and y intercept, we get the line for the equation $x+2y=4$

Graphing the equation $2x-y=3$:

To graph the equation $2x-y=3$, let us determine the x and y intercepts.

x - intercept: When y = 0, then $2x-0=3 \implies x=-1.5$

y - intercept: When x = 0, then $2(0)-y=3 \implies y=-3$

The coordinates are (-1.5,0) and (0,-3)

Thus, joining the coordinates of x and y intercepts, we get the line for the equation $2x-y=3$

Solution:

The solution of the two equations is the point of intersection of two lines in the graph.

Let us determine the solution using substitution method.

Substituting $x=4-2y$ in the equation $2x-y=3$, we get;

$2(4-2y)-y=3$

    $8-4y-y=3$

          $8-5y=3$

             $-5y=-5$

                  $y=1$

Thus, the value of y is 1.

Substituting $y=1$ in the equation $2x-y=3$, we have;

$2x-1=3$

     $2x=4$

       $x=2$

Thus, the value of x is 2.

Therefore, the solution of the system of equations is (2,1)