Let's solve find the value of x in each set of equations, we can do this by following this steps:
1. solve for y from the first equation
2. replace the expression we found into the second equation
3.solve for x
a) 2x+y=10 and x-3y= -2
step 1.
2x+y=10, then:
2x-2x+y=10-2x, then:
y=10-2x
step 2.
x-3y= -2, then:
x-3(10-2x)= -2, then:
x-30+6x= -2, then:
7x-30= -2
7x-30+30= -2+30
7x=28
7x/7=28/7, then:
x= 28/7=3
b) 2x + y= 10 and -6x -3y= -2
This system of equations does not have a single solution
c) x+2y= 5 and 2x + y = 4
step 1.
x+2y= 5
x-x+2y=5-x
2y=5-x
y=(5-x)/2
step 2
2x + y = 4
2x+(5-x)/2=4
2x+5/2-x/2=4
(2-1/2)x+5/2=4
3/2x+5/2=4
3/2x+5/2-5/2=4-5/2
3/2x=4-5/2
3/2x=3/2
x=1
d) 5x+ y= 33 and x=18-4y
applying the same steps
x=6
e) Y=13 -2x and 8x + 4y =52
This system of equations does not have a single solution
f)x+ 3y =5 and 6x-y=11
applying the same steps
x=2
g) Y=10 + x and 2x + 3y =45
applying the same steps
x=3
If we arrange the systems of equations in increasing order of x, we get:
1)
x+2y= 5
2x + y = 4
2)
x+ 3y =5
6x-y=11
3)
Y=10 + x
2x + 3y =45
and
2x+y=10
x-3y= -2
4)
5x+ y= 33
x=18-4y