Respuesta :
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:
[tex]\begin{gathered} \frac{-19x}{-19}=\frac{95}{-19} \\ \\ x=-5 \end{gathered}[/tex]• 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:
[tex]\begin{gathered} \frac{-y}{-1}=\frac{-3}{-1} \\ \\ y=3 \end{gathered}[/tex]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)
