The system of equations from the image is:

1. $3x + 4y = 14$
2. $5x + 2y = 21$

We can solve these equations using substitution or elimination. I'll use the elimination method:

Step 1: Multiply the equations to align coefficients

To eliminate $y$, multiply the first equation by 2 and the second equation by 4:

$2(3x + 4y) = 2(14) \implies 6x + 8y = 28$ $4(5x + 2y) = 4(21) \implies 20x + 8y = 84$

Step 2: Subtract the equations

$(20x + 8y) - (6x + 8y) = 84 - 28$ $14x = 56$ $x = 4$

Step 3: Substitute $x = 4$ into one of the original equations

Substitute into $3x + 4y = 14$: $3(4) + 4y = 14$ $12 + 4y = 14$ $4y = 2$ $y = \frac{1}{2}$

Final Solution:

$x = 4, \, y = \frac{1}{2}$

Would you like a detailed explanation of the method or a graph of the system?

Related Questions:

1. How can elimination be applied to systems with larger coefficients?
2. What are the steps to verify the solution for this system?
3. How can substitution help in solving the same system of equations?
4. What happens if the system is inconsistent or dependent?
5. Can you explain how to solve these equations graphically?

Tip:

Always double-check your solution by substituting $x$ and $y$ into the original equations to confirm both equations are satisfied.