Question

What is the solution to the system of equations below?

A) (-2.5, -1)
B) (-1, -2.5)
C) (1, 2.5)
D) (2.5, 1)

Answer 1

The solution to the system of equations is (x, y) = (\(\frac{-95}{23}\), \(\frac{36}{23}\)). In decimal form, this is approximately (-4.13, 1.57).

Step-by-step explanation:

To find the solution to the system of equations, we need to solve the equations simultaneously. The system of equations can be written as:

x = -2y - 1

2x + 5y = 10

We can solve this system using the substitution or elimination method. Let's use the elimination method:

1. Multiply the first equation by 2 to make the coefficients of x in both equations equal:

• 2x = -4y - 2

Add the two equations:

• (-4y - 2) + (2x + 5y) = 10
• -4y + 2x + 5y = 10

Simplify the equation:

• 2x + y = 12

Multiply the first equation by 5 to make the coefficients of y in both equations equal:

• 5x = -10y - 5

Add the two equations:

• (-10y - 5) + (5x + y) = 12
• -10y + 5x + y = 12

Simplify the equation:

• 5x - 9y = 12

Now we have a new system of equations:

2x + y = 12

5x - 9y = 12

Let's solve this system using the elimination method:

1. Multiply the first equation by 5:

• 10x + 5y = 60

Multiply the second equation by 2:

• 10x - 18y = 24

Subtract the second equation from the first equation:

• (10x + 5y) - (10x - 18y) = 60 - 24
• 23y = 36

Now we can solve for y:

y = \(\frac{36}{23}\)

Substitute this value back into either of the original equations to solve for x. Let's use the first equation:

1. x = -2y - 1
2. x = -2(\(\frac{36}{23}\)) - 1
3. x = -\(\frac{72}{23}\) - 1
4. x = \(\frac{-72 - 23}{23}\)
5. x = -\(\frac{95}{23}\)

Therefore, the solution to the system of equations is (x, y) = (\(\frac{-95}{23}\), \(\frac{36}{23}\)). In decimal form, this is approximately (-4.13, 1.57).