Question 1203037
here's what i get.
your equations that need to be solve simultaneously are:
x + y = -4
y = 2x - 1
we'll use the substitution method.
in the first equation, replace y with 2x - 1 from the second equation to get:
x + 2x - 1 = -4
add 1 to both sides of the eeuation and combine like terms to get:
3x = -3
solve for x to get x = 1-1
in the second equation, replace x with -1 and solve for y to get:
y = 2*-1 - 1 = -3
your solution to this equation is x = -1 and y = -3
replace x with -1 and y with -3 in both equations to ge:
x + y = -4 becomes -1 + -3 = -4 which becomes -4 = -4 which is true.
y = 2x - 1 becomes -3 = 2*-1 - 1 which becomes -2 -1 = -3 which becomes -3 = -3 which is true.
both equations are true when x = -1 and y = -3.
the graph of these equations is shown below.


<img src = "http://theo.x10hosting.com/2023/071401.jpg">



A system of simultaneous linear equations can have either: one unique solution, infinitely many solutions or no solutions.


from a graphical standpoint, the unique solution is where the lines intersect; infinitely many solution are when the lines are identical, i.e. both equations form the same equivalent equation which generates the same line for both; no solutions are whn the lines are parallel to each other.


theee are ptjer waus to describe the solutions as noted in the following reference.
<a href = "https://ionamaths.weebly.com/uploads/1/4/2/0/14204419/consistencyanddependency.pdf" target = "_blank">https://ionamaths.weebly.com/uploads/1/4/2/0/14204419/consistencyanddependency.pdf</a>


i think that about covers it.
let me know if you need more.
theo