Question

Solve the following system of equations.5x - y = - 286x- 5y= -45

Answer 1

Given the system of equations:

• 5x - y = -28

,

• 6x - 5y = -45

Let's solve the system of equations using the addition and elimination method.

To solve, apply the following steps:

• Step 1.

Multiply each equation by the value that makes the coefficient of one variable opposite.

Multiply equation 1 by -5.

We have:

-5 (5x - y) = -5(-28) ==> -5(5x) -5(-y) = 140 ===> -25x + 5y = 140

• Step 2:

Add both equations:

-25x + 5y = 140

+ 6x - 5y = -45

__________________

-19x + 0 = 95

-19x = 95

• Step 3:

Divide both sides by -19:

`\begin{gathered} (-19x)/(-19)=(95)/(-19) \\ \\ x=-5 \end{gathered}`

• Step 4:

Substitute -5 for x in either of the equations.

5x - y = -28

5(-5) - y = -28

-25 - y = -28

Add 25 to both sides of the equation:

-25 + 25 - y = -28 + 25

-y = -3

Divide both sides by -1:

`\begin{gathered} (-y)/(-1)=(-3)/(-1) \\ \\ y=3 \end{gathered}`

Therefore, the solution to the system of equations is:

x = -5, y = 3

ANSWER:

x = -5, y = 3

In point form:

(x, y) ==> (-5, 3)