Answers:
In other words, x = 3 and y = 3
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Explanation:
Let's solve the first equation for x. I'm picking on this equation variable because the coefficient is 1.
Solving for x leads to
x-2y = -3
x = -3+2y
I added 2y to both sides
Now we'll plug this into the other equation. This means we replace every copy of x with -3+2y since they are the same thing.
3x + 5y = 24
3( x ) + 5y = 24
3( -3+2y ) + 5y = 24 .... replace x with -3+2y
3(-3) + 3(2y) + 5y = 24 .... distribute
-9 + 6y + 5y = 24
11y-9 = 24
11y-9+9 = 24+9 ...... adding 9 to both sides
11y = 33
11y/11 = 33/11 .... dividing both sides by 11
y = 3
We'll use this y value to find x. We can pick on any equation with x & y in it, but I find it's easiest to use the equation where x is isolated
x = -3+2y
x = -3+2(3) .... replace y with 3
x = -3+6
x = 3
So both x and y are equal to 3
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Let's check the answer
Plug (x,y) = (3,3) into the first equation. We should get the same number on both sides after simplifying fully
x-2y = -3
3 - 2(3) = -3
3 - 6 = -3
-3 = -3
So far, so good. Let's try the other equation
3x + 5y = 24
3(3) + 5(3) = 24
9 + 15 = 24
24 = 24
The other equation is true as well. This fully confirms that (x,y) = (3,3) is the solution to this system of equations. If you graphed each original equation, you should find they cross at the location (3,3).
Side note: it won't always be the case that x and y are the same value.
