Question

Which graph represents the solution to the given system? y = -2x + 5 and y = 3x - 2

Answer 1

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

$y=mx+b$

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

The given system of equations is

$y=-2x+5$             .... (1)

$y=3x-2$              .... (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).

$-2x+5=3x-2$

Isolate the variable terms.

$-2x-3x=-5-2$

$-5x=-7$

Divide both sides by -5.

$\frac{-5x}{-5}=\frac{-7}{-5}$

$x=1.4$

Substitute x=1.4 in equation (1).

$y=-2(1.4)+5$

$y=-2.8+5$

$y=2.2$

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).

Answer 2

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