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).
