Final answer:
To solve the system of equations 2x+3y=16 and 5x-2y=21, multiply the first equation by 2, the second equation by 3, add the two equations, solve for x, substitute the value of x into either equation, and solve for y. The solution is x = 5 and y = 2.
Step-by-step explanation:
To solve the system of equations:
2x + 3y = 16
5x - 2y = 21
Step 1: Multiply the first equation by 2:
4x + 6y = 32
Step 2: Multiply the second equation by 3:
15x - 6y = 63
Step 3: Add the two equations:
19x = 95
Step 4: Solve for x:
x = 5
Step 5: Substitute the value of x into either equation (let's use the first equation):
2(5) + 3y = 16
10 + 3y = 16
Step 6: Solve for y:
3y = 6
y = 2
Therefore, the solution to the system of equations is x = 5 and y = 2.