Question

solve using elim -x - 5y = 11 3x + 5y = -3

Explanation:

Step1: Add the two equations

We have the system of equations:
$$-x - 5y = 11$$
$$3x + 5y = -3$$
Adding the left - hand sides and the right - hand sides of the two equations respectively, we get:
$$(-x - 5y)+(3x + 5y)=11+(-3)$$
Simplify the left - hand side: $-x - 5y+3x + 5y=(-x + 3x)+(-5y + 5y)=2x$
Simplify the right - hand side: $11-3 = 8$
So, $2x=8$

Step2: Solve for x

Divide both sides of the equation $2x = 8$ by 2:
$$x=\frac{8}{2}=4$$

Step3: Substitute x = 4 into one of the original equations to solve for y

Let's substitute $x = 4$ into the first equation $-x - 5y=11$:
$$-4-5y = 11$$
Add 4 to both sides of the equation:
$$-5y=11 + 4$$
$$-5y=15$$
Divide both sides by - 5:
$$y=\frac{15}{-5}=-3$$

Answer:

The solution to the system of equations is $x = 4$ and $y=-3$