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

1.75 I think j hope it helps!...

Solve the following systems by graphing. 1. x

ashleychantal99

23.01.2022

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)

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