Explanation:
To solve the system of equations:
3x - 4y = 16
2x + 3y = 5
We can use either substitution or elimination method. Here, we will use the elimination method:
Multiply the second equation by 4 to get:
8x + 12y = 20
Now we can add this equation to the first equation:
3x - 4y + 8x + 12y = 16 + 20
Simplifying the left side and adding the right side, we get:
11x = 36
Dividing both sides by 11, we get:
x = 36/11
Substituting this value of x into the second equation, we get:
2(36/11) + 3y = 5
Multiplying through by 11 to eliminate the fraction, we get:
72/11 + 3y = 55/11
Subtracting 72/11 from both sides, we get:
3y = -17/11
Dividing both sides by 3, we get:
y = -17/33
Therefore, the solution to the system of equations is:
x = 36/11, y = -17/33
or in decimal form,
x ≈ 3.27, y ≈ -0.52