Answer:
for x=2 , y=5 and x=[tex]\frac{-1}{2}[/tex] , y= [tex]\frac{-5}{2}[/tex]
Step-by-step explanation:
Given : y = 2x² - 3 and y = 3x - 1.
To find : Solve the system of equations.
Solution : We have given that
y =2x² - 3 ---------(equation number 1)
y = 3x - 1. ----------(equation number 2)
Substitute the equation 1 in equation 2
2x² -3 = 3x -1
On subtracting both side by 3x.
2x² -3 -3x =3x -1 -3x
2x² -3 -3x = -1
On adding both side by 1.
2x² -3 -3x +1 = -1 +1
2x² -3x -2 = 0
On factoring
2x² -4x +x -2 = 0
Taking common 2x from fisrt two term and 1 from last two term.
2x(x-2) +1 (x-2) =0
On grouping
(2x+1) (x-2) =0
2x+1 =0
x=[tex]\frac{-1}{2}[/tex]
x-2 =0
x=2
Plugging x=2 in second term.
y= 3x-1
y=3*2-1
y=5
Plugging x= - 1/2 in second term.
y= 3x-1
y=3([tex]\frac{-1}{2}[/tex]) -1
y=[tex]\frac{-5}{2}[/tex]
Therefore , for x=2 , y=5 and x=[tex]\frac{-1}{2}[/tex] , y= [tex]\frac{-5}{2}[/tex]
