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Arrange the systems of equations that have a single solution in increasing order of x-values in their solutions. 2x+y=10x-3y=-22x + y= 10-6x -3y=-2x+2y= 52x + y = 45x+ y= 33x=18-4yY=13 -2x8x + 4y =52x+ 3y =56x-y=11Y=10 + x 2x + 3y =45

1 Answer

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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

User Michpohl
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