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  

-      -         -

___________

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

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.