Please help me solve this problem

Question

If x+5y=-11 and 2x-3y=17. What is the value of x and y?

Answer 1

Both equations are lines. That means, if you want to find a solution that works for both of them, you are looking for the intersection of the two lines. That point will lie on both lines.

There are several ways to solve this system of equations. One way is called substitution. Write one equation as x = (something) or y = (something), then substitute that "something" into the other equation.

In this case, we have x + 5y = -11 and we can subtract 5y from both sides to get x = -5y -11. Now, we can use that in the second equation. We take 2x - 3y = 17 and wherever we see an "x", we replace it (or substitute) "-5y -11" because x = -5y -11. That makes the equation:

2(-5y -11) - 3y = 17

Now multiply that out to get:

-10y -22 - 3y = 17

Combine like-terms to get:

-13y - 22 = 17

Add 22 to both sides to get:

-13y = 39

Divide by -13 to get:

y = -3

Now, plug -3 in for y in the original equation we had which was x = -5y -11 to get:

x = -5(-3) - 11

or x = 15 - 11

or x = 4.

So x = 4 and y = -3 or the intersection point of the two lines is the point (4, -3)

Answer 2

Multiply the first equation by 2.

Subtract the 2nd equation from this one to get: 13y=-39.

You take it from here.