Question

How do you work out this equation

solve simultaneous equations by substitution
9x - 2y = -1
2y = 3x - 5

Answer 1

x is equal to negative one, and y is equal to negative four.

Explanation:

You can do this by solving one of the equations by either x or y, then substituting it into the other. Let's solve the second one for y:

`2y = 3x - 5\\y = (3x - 5)/(2)`

Now we'll substitute that into the first equation:

`9x - 2y = -1\\9x - 2((3x - 5)/(2)) = -1\\9x - 3x + 5 = -1\\6x + 5 = -1\\6x = -6\\x = -1`

So we now know that x is equal to -1. We can simply substitute that into one of the original equations to find y:

`2y = 3x - 5\\2y = 3(-1) - 5\\2y = -3 - 5\\2y = -8\\y = -4`

We now know that x is equal to -1, and y is equal to -4. We can also check our answer by plugging that -4 into the other equation, and see if we still get -1:

`9x - 2y = -1\\9x - 2(-4) = -1\\9x + 8 = -1\\9x = -1 - 8\\9x = -9\\x = -1`

So we know that our answer is correct.