Question

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

Answer 1

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 2

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).

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.

`(-5x)/(-5)=(-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).