Respuesta :

MaharaniP
To find the X value of the solution, you would set the two equations equal to each other bu substitution:
if y = -2x + 5 and y = 3x - 2, 
-2x + 5 must be equal to 3x - 2
solve for x... you should get 7/5

then, plug that into one of the original equations as X and you would get the Y value, 11/5

This point, (7/5,11/5) is where the two lines cross

Answer:

The solution of given system of equations is (1.4, 2.2). It means the graph of both lines intersect each other at (1.4, 2.2).

Step-by-step explanation:

The slope intercept form of a line is

[tex]y=mx+b[/tex]

where, m is slope and b is y-intercept.

The given system of equations is

[tex]y=-2x+5[/tex]             .... (1)

[tex]y=3x-2[/tex]              .... (2)

The slope of equation (1) is -2 and y-intercept is 5.

The slope of equation (2) is 3 and y-intercept is -2.

Equate equation (1) and  (2).

[tex]-2x+5=3x-2[/tex]

Isolate the variable terms.

[tex]-2x-3x=-5-2[/tex]

[tex]-5x=-7[/tex]

Divide both sides by -5.

[tex]\frac{-5x}{-5}=\frac{-7}{-5}[/tex]

[tex]x=1.4[/tex]

Substitute x=1.4 in equation (1).

[tex]y=-2(1.4)+5[/tex]

[tex]y=-2.8+5[/tex]

[tex]y=2.2[/tex]

Therefore, the solution of given system of equations is (1.4, 2.2). It means the graph of both lines intersect each other at (1.4, 2.2).

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