• 1.
x+y=3
2x+2y= 6
Multiply the first equation by 2, and then subtract both equations.
2x+2y=6
-
2x+2y=6
_______
0x+0y=0
0
Since both variables are eliminated, there are INIFINITE SOLUTIONS
• 2.
y= 2x-3
-2x+y=6
Put the first equation into the second equation, (replace y )
-2x+(2x-3) = 6
Solve for x
-2x+2x-3=6
-3= 6
Since -3 is not equal to 6, there is NO SOLUTION.
• 3.
X+3y = 14
-5x+6y=-28
Multiply the first equation by 2, then subtract the equations:
2x+6y=28
-
-5x+6y=-28
_________
7x= 56
x= 56/7
x= 8
Replace x=8 on any equation and solve for y:
8+3y= 14
3y=14-8
3y= 6
y=6/3
y=2
Solution = (8,2)
• 4.
-1/2x+3y=23
y=5x-2
Put the second equation into the first equation ( replace y) and solve for x
-1/2x + 3 (5x-2)= 23
-1/2x+ 15x - 6 = 23
-1/2x +15x = 23+ 6
29/2 x = 29
x = 29/ (29/2)
x = 2
Replace x on any equation and solve for y
y= 5x-2
y=5(2)-2
y= 10-2
y=8
Solution: (2,8)
