Is (4,1) a solution to the equation y=-x+3 ?

The given points ( 4 , 1 ) is not a solution of line y = - x + 3  .

Step-by-step explanation:

Given line equation as :

y = - x + 3

Now to get the solutions of line equation , we have to substitute the x-coordinate value and y-coordinate value in the given line equation , and if the coordinates satisfy the equation, then this must be the solution .

So , for points ( 4 , 1 )

Here x-coordinate is 4

And y-coordinate is 1

∴ For x = 4 , The line is y = - 4 + 3

I.e y = - 1

And For y = 1 , The line is 1 = - x + 3

I.e x = 3 - 1 = 2

So, We have check both the coordinates but they do not satisfy the line equation

Hence The given points ( 4 , 1 ) is not a solution of line y = - x + 3  . Answer

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!