Answer:
The solution of the system is the point (2,-1)
Step-by-step explanation:
we know that
The equation of the line in slope -intercept form is equal to
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
we have
[tex]2x+y=3[/tex]
Isolate the variable y
subtract 2x both sides
[tex]y=-2x+3[/tex] ----> equation A
[tex]-2y=14-6x[/tex]
isolate the variable y
Multiply by -1 both sides
[tex]2y=6x-14[/tex]
Divide by 2 both sides
[tex]y=3x-7[/tex] -----> equation B
we have
[tex]y=-2x+3[/tex] ----> equation A
[tex]y=3x-7[/tex] -----> equation B
solve the system by substitution
substitute equation A in equation B
[tex]3x-7=-2x+3[/tex]
solve for x
[tex]3x+2x=7+3\\5x=10\\x=2[/tex]
Find the value of y
[tex]y=-2(2)+3=-1[/tex]
therefore
The solution of the system is the point (2,-1)
