Find the intersection of the lines 2x+5y=8 and 6x+y=10 in two ways by elimination and by substitution, step by step .

The lines intersect at x = 1.5 and y = 1

Step-by-step explanation:

We need to find  the intersection of the lines 2x+5y=8 and 6x+y=10.

We need to find the values of x and y by elimination and by substitution.

a) By Elimination:

2x+5y = 8     (1)

6x + y = 10    (2)

Multiply eq(2) with 5 and subtract eq(1) from(2)

30x + 5y = 50

2x   + 5y = 8  

-      -         -

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28x = 42

x = 1.5

Now putting value of x in eq(2)

6x + y = 10

6(1.5) + y = 10

9 + y = 10

=> y = 10 - 9

y = 1

so, (x,y) = (1.5,1)

The lines intersect at x = 1.5 and y = 1

b) By substitution

2x+5y = 8     (1)

6x + y = 10    (2)

Finding value of y in equation 2 and substituting in eq(1)

y = 10 -6x

2x + 5(10 - 6x) = 8

2x + 50 - 30x = 8

-28x = 8-50

-28x = -42

x = -42/-28

x = 1.5

Now finding value of y by substituting value of x

6x + y = 10

6x = 10-y

x = 10 - y /6

2x + 5y = 8

2(10-y/6) + 5y = 8

10-y/3 + 5y = 8

10 -y +15y/3 = 8

10 +14y = 8*3

+14 y = 24 -10

+14 y =  14

y = 14/14

y = 1

So, (x,y) = (1.5,1)

The lines intersect at x = 1.5 and y = 1

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