Question

the sum of two numbers is -1. when twice the first number and four times the second number are added the sum is -10.what are the two numbers

Answer 1

Answer:

3 and - 4

Step-by-step explanation:

Let

The first number be "x", and

The second number be "y"

The sum of the 2 numbers is -1, so we can write:

x + y = -1

or

x = -1 - y

Twice the first and 4 times second SUMMED, gives us -10, so we can write:

2x + 4y = -10

Now, we put 1st equation in 2nd and find y first:

$2x + 4y = -10\\2(-1-y) + 4y = -10\\-2-2y+4y=-10\\2y=-10+2\\2y=-8\\y=-4$

Now, finding x:

x = -1 - y

x = -1 -(-4)

x = -1 + 4

x = 3

So, the two number are:

3 and - 4

Answer 2

Answer:

The number are: $x=3$ and $y=-4$

Step-by-step explanation:

Let us consider the numbers be $x$ and $y$.

As the sum of two numbers is $-1.$

So,

$x + y = -1$

and

Twice the first number and four times the second number are added the sum is $-10$.

So,

$2x + 4y = -10$

Solving

$x + y = -1$

$2x + 4y = -10$

$\begin{bmatrix}x+y=-1\\ 2x+4y=-10\end{bmatrix}$

$\mathrm{Subsititute\:}x=-1-y$

$\begin{bmatrix}2\left(-1-y\right)+4y=-10\end{bmatrix}$

$-2-2y+4y=-10$

$2y=-8$

$y=-4$

$\mathrm{Subsititute\:}y=-4$

$x=-1-(-4)$

$x=3$

Therefore, the number are: $x=3$ and $y=-4$

Verification:

As $x=3$ and $y=-4$

So,

$x + y = -1$

$3 + (-4) = -1$

$-1=-1$

Also

$2x + 4y = -10$

$2(3) + 4(-4)= -10$

$6-16=-10$

$-10=-10$

Keywords: number, equation

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