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Select the correct answer.
What is the exact solution to the system of equations shown on the graph?
-5
5
A. (-1,4)
B. (-1,4)
C. (-1,6)
D. (-1,4)

Select the correct answer What is the exact solution to the system of equations shown on the graph 5 5 A 14 B 14 C 16 D 14 class=

Respuesta :

roohafzah

Answer :

  • B. (-1⅕,4⅗)

Explanation :

Let's name the solution of the system as 'T'

first, let's find the equations of the two lines using any two points they pass through

line A

(-2,3) and (0,7)

first, let's find the slope of the line

  • m = (y2-y1)/(x2-x1)

m = (7-3)/(0+2)

m = 4/2

m = 2

now ,plug the value of m and either of the points in the equation below

  • y - y1 = m(x-x1)

y - 3 = 2(x - (-2))

y - 3 = 2x + 4

now , simplify to the point slope form ( y = mx + b)

y = 2x + 4 + 3

  • y = 2x + 7 ....(1)

similarly,

line B

(2,-5) and (0,1)

find the slope

m = (y2-y1)/(x2-x1)

m = (1 - (-5))/(0-2)

m = 6/-2

m = -3

now ,plug the value of m and either of the points in the equation below

  • y - y1 = m(x-x1)

y - 1 = -3(x - 0)

simplify to the point slope form ( y = mx + b)

  • y = -3x + 1 ....(2)

from eq(1) and eq(2)

2x + 7 = -3x +1

2x + 3x = 1 - 7

5x = -6

x = -6/5

  • x = -1⅕

plug in the value of x in either of the equations

y = 2*(-6/5) + 7

y = -12/5 + 7

y = (-12 + 35)/5

y = 23/5

  • y = 4⅗

thus, the solution of the system is at point T(-1⅕,4⅗).

semsee45

Answer:

[tex]\sf B.\quad \Large\text{$\left(-1\frac15,4\frac35\right)$}[/tex]

Step-by-step explanation:

The exact solution to a graphed system of linear equations is the point of intersection of the two lines.

To find the solution of the graphed system of equations, first find the equation of each line by entering its slope and y-intercept into the slope-intercept form of a linear equation:

[tex]\boxed{\begin{array}{l}\underline{\textsf{Slope-intercept form of a linear equation}}\\\\y=mx+b\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$m$ is the slope.}\\\phantom{ww}\bullet\;\;\textsf{$b$ is the $y$-intercept.}\\\end{array}}[/tex]

The line with the positive slope crosses the y-axis at y = 7 and has a slope of 2, since the y-values increase by 2 units for every 1 unit increase in x-values. Therefore, the equation of this line is:

[tex]y = 2x + 7[/tex]

The line with the negative slope crosses the y-axis at y = 1 and has a slope of -3, since the y-values decrease by 3 units for every 1 unit increase in x-values. Therefore, the equation of this line is:

[tex]y=-3x+1[/tex]

To find the x-coordinate of the point of intersection, substitute the first equation into the second equation and solve for x:

[tex]2x+7=-3x+1\\\\\\5x=-6\\\\\\x=-\dfrac{6}{5}\\\\\\x=-1\frac15[/tex]

Now, substitute x = -6/5 into one of the equations and solve for y. Let's use y = 2x + 7:

[tex]y = 2\left(-\dfrac{6}{5}\right)+ 7\\\\\\y = \dfrac{-12}{5}+\dfrac{35}{5}\\\\\\y=\dfrac{23}{5}\\\\\\y=4\frac35[/tex]

Therefore, the exact solution to the graphed system of equations is:

[tex]\Large\text{$\left(-1\frac15,4\frac35\right)$}[/tex]

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