What is the value of x and y in this equation 2x plus 3y equals -5 and 5x plus 2y equals 4 The number for x and y stay the same for both parts of the equation?

Answer 1

This is a system of equations, and we can use various methods to solve it. We'll use substitution in this case. We're told:

2x + 3y = -5

5x + 2y = 4

To solve by substitution, what we need to do is take either one of those equations, and solve it for either x or y. Let's take the second one and solve it for x:

5x + 2y = 4

5x = 4 - 2y

x = (4 - 2y)/5

Now we can take that solution for x, and substitute it into the other equation:

2x + 3y = -5

2((4 - 2y)/5) + 3y = -5

(8 - 4y) / 5 + 3y = -5

(8 - 4y + 15y) / 5 = -5

8 - 4y + 15y = -25

11y = -33

y = -3

We now have a value for y, and can plug it into either of the original equations to solve for x:

2x + 3y = -5

2x + 3(-3) = -5

2x - 9 = -5

2x = 4

x = 2

To verify our answer, we can plug either x or y into the other of our original equations, and see if we get the same result for the other variable:

5x + 2y = 4

5(2) + 2y = 4

10 + 2y = 4

2y = -6

y = -3

So that confirms our answer, and the two equations intersect at the point (2, -3).