Question

I dont understand step by step explanation pls it’s also asking for a solution

Answer 1

We have two equations, since both of them are linear in x and y we conclude that this is are lines. To find their slope we need to write them in the slope-intercept form:

`y=mx+b`

Line x-y=2

Let's write the equation in slope intercept form:

`\begin{gathered} x-y=2 \\ y=x-2 \end{gathered}`

Comparing the last line with the slope intercept form we conclude that the slope of this line is 1.

Now, to find the values of y given a value of x we just need to plug the value of x we want and find its corresponding value of y with the equation; for example, if x=0, then we have:

`\begin{gathered} y=0-2 \\ y=-2 \end{gathered}`

Following this procedure we have that:

To graph the line we plot this points on the plane and join them with a straight line:

Line 3x-4y=9

Following the same procedure as with the previous line we have that this line can be written as:

`\begin{gathered} 3x-4y=9 \\ 4y=3x-9 \\ y=(3)/(4)x-(9)/(4) \end{gathered}`

Hence the slope of this line is 3/4.

The table we get in this case is:

Plotting this points and joining with a straight line we get the graph of the equation:

Graphical solution.

To find the solution of the system graphically we need to graph both lines in the same plane; the solution of the system is the point where the lines intersect. Let's do that:

From the graph we notice that the intersection happens at the point (-1,-3).

Therefore, the solution of the system is the point (-1,-3) which means that x=-1 and y=-3

Algebraic solution.

To find the solution of the system:

`\begin{gathered} x-y=2 \\ 3x-4y=9 \end{gathered}`

we solve the first equation for y:

`y=x-2`

and plug this in the second equation:

`\begin{gathered} 3x-4(x-2)=9 \\ 3x-4x+8=9 \\ -x=9-8 \\ -x=1 \\ x=-1 \end{gathered}`

once we have the value of x we plug it in the expression of y:

`\begin{gathered} y=-1-2 \\ y=-3 \end{gathered}`

Therefore, we have that x=-1 and y=-3 just like we gound graphically