Write the slope-intercept form of the equation for the line. a.y = 2x – 1 b.y = 1/2x + 1 c.y = –2x – 1 d.y =1/2 x – 1

The solution to the system of equation 4x - 9y = -42 and x + 5y = 4 is x = -6 and y = 2.

What is the solution to the system of equations?

Given the system of equations in the question:

4x - 9y = -42

x + 5y = 4

To solve the system of equations using the elimination method, first multiply the second equation by 4:

4[ x + 5y = 4 ] → 4x + 20y = 16

Hence, we have:

4x - 9y = -42

4x + 20y = 16

Subtract the first equation from the second equation to eliminate 4x:

0 - 29y = -58

29y = 58

y = 58/29

y = 2

Plug y = 2 into equation 2 and solve for x;

x + 5y = 4

x + 5(2) = 4

x + 10 = 4

x = 4 - 10

x = -6

Therefore, the value of x is -6 and y is 2.

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Answer:

x = -6 and y = 2

Step-by-step explanation:

4x-9y = -42

x+5y = 4

4x-9y = -42

4x + 20y = 16

Take them away from each other.

-29y = -58

Find what one y is by dividing.

-58 / -29 = 2

y = 2

Substitute back into original.

x + 10(5*y) = 4

Take 10 away to find x.

x = -6

Check if answer is correct.

4x - 9y = -42

-24 - 18 = -42

Final Answer: x = -6 and y = 2

We have to use the property of rhombus that diagonals bisects each other and form 90 degree.

So we have to use pythagorean identity here

x=12

So the other diagonal is 12*2=24.

And area of rhombus =0.5(product of diagonals)

=0.5*10*24 =120