Answer:
(-13/5,-12/5)
Explanation:
To solve the system of two linear equations below algebraically using elimination:
x + 5y = -17
x - 3y = 7
We can use the elimination method by adding the two equations together to eliminate the x term. When we add the two equations, the x term cancels out:
(x + 5y) + (x - 3y) = -17 + 7
2x + 2y = -10
We can simplify the equation by dividing both sides by 2:
x + y = -5
Now we have one equation with one variable. We can substitute this equation into one of the original equations to solve for the other variable. Let's use the first equation:
x + 5y = -17
Substitute x + y for x:
(x + y) + 5y = -17
Simplify by combining like terms:
x + 6y = -17
Now we have two equations:
x + y = -5
x + 6y = -17
We can use the elimination method again by subtracting the first equation from the second equation:
(x + 6y) - (x + y) = -17 - (-5)
5y = -12
Divide both sides by 5:
y = -12/5
Now that we know the value of y, we can substitute it into one of the original equations to solve for x. Let's use the first equation:
x + y = -5
Substitute y = -12/5:
x - 12/5 = -5
Add 12/5 to both sides:
x = -13/5
So the solution to the system of equations is:
x = -13/5
y = -12/5
Therefore, the solution to the system of equations using elimination is (x,y) = (-13/5,-12/5).