Question

N8) solve the system using substitution method and then graph the equations.2x - 4y = -23x + 2y = 3-

Answer 1

Given:

2x - 4y = -2

3x + 2y = 3

Substitution method

`\begin{gathered} From\text{ 3x+2y=3} \\ 3x=3-2y \\ x=(3-2y)/(3) \end{gathered}`
`\begin{gathered} Substitute\text{ }x=(3-2y)/(3)\text{ into the first equation} \\ 2x-4y=-2 \\ 2((3-2y)/(3))-4y=-2 \\ (6-4y)/(3)-4y=-2 \\ Multiply\text{ }trough\text{ by 3} \\ 6-4y-12y=-6 \\ 6-16y=-6 \\ -16y=-6-6 \\ -16y=-12 \\ y=(-12)/(-16) \\ y=(3)/(4) \end{gathered}`
`\begin{gathered} Substitute\text{ y=}(3)/(4)\text{ into }x=(3-2y)/(3) \\ x=(3-2((3)/(4)))/(3)=(3-(3)/(2))/(3)=((6-3)/(2))/(3)=((3)/(2))/(3) \\ x=(3)/(6) \\ x=(1)/(2) \end{gathered}`
`Thus,\text{ x=}(1)/(2),y=(3)/(4)`

Graphical method:

Plot the graph of the two equations on the same graph

The point of intersection of the two graphs gives the solution to the system of equations

The point of intersection is (0.5, 0.75)

Which in fraction gives (1/2, 3/4)

Thus. x = 1/2, y= 3/4