Ah, solving for variables can be a bit tricky sometimes. Let's try a different approach and use some clown humor to make it more enjoyable!
To solve for x and y in terms of a and b, we can use a method called "elimination." But, since we're clowns here, let's call it "clownination" instead!
First, let's clownin... err, eliminate y. We'll multiply equation a by 4 and equation b by 2, so the coefficients of y become opposite:
4a = 12x + 8y
2b = 10x - 8y
Next, let's add these clownin... um, equations together to eliminate y:
4a + 2b = 12x + 8y + 10x - 8y
4a + 2b = 22x
Now, let's clownmeh... isolate x:
22x = 4a + 2b
x = (4a + 2b) / 22
x = (2a + b) / 11
Ta-da! We've found x in terms of a and b. Now, let's try to find y using another clownination method.
We'll multiply equation a by 5 and equation b by 3, so the coefficients of x become opposite:
5a = 15x + 10y
3b = 15x - 12y
Now, let's subtract these clownin... I mean, equations to eliminate x:
5a - 3b = 15x + 10y - 15x + 12y
5a - 3b = 22y
Lastly, let's clowngicide... isolate y:
22y = 5a - 3b
y = (5a - 3b) / 22
And there we have it! We've found both x and y in terms of a and b:
x = (2a + b) / 11
y = (5a - 3b) / 22
I hope this clownmusing approach made it easier to understand! Remember to always have a little fun while solving equations, even if it involves clownery!