The system of equations is:

1. $-4x + 2y = 0$
2. $10x + 3y = 8$

Let's solve it using the substitution method.

Step 1: Solve one equation for one variable

From equation 1 ($-4x + 2y = 0$), solve for $y$:

$-4x + 2y = 0$ 2y = 4x \quad \text{(add 4x to both sides)} $y = 2x \quad \text{(divide by 2)}$

Step 2: Substitute $y = 2x$ into equation 2

Substitute $y = 2x$ into $10x + 3y = 8$:

$10x + 3(2x) = 8$ $10x + 6x = 8$ $16x = 8 \quad \text{(combine like terms)}$ $x = \frac{8}{16} = \frac{1}{2}$

Step 3: Substitute $x = \frac{1}{2}$ into $y = 2x$

Now substitute $x = \frac{1}{2}$ into $y = 2x$:

$y = 2\left(\frac{1}{2}\right) = 1$

Final Solution:

The solution to the system is: $x = \frac{1}{2}, \quad y = 1$

Would you like a step-by-step verification or further clarification?

5 Related Questions:

1. How would you solve this system using the elimination method?
2. What happens if the system of equations has no solution or infinitely many solutions?
3. How can you graphically interpret the solution $x = \frac{1}{2}, y = 1$?
4. What other methods, besides substitution and elimination, can solve a system of equations?
5. How does substituting $y = 2x$ simplify the problem?

Tip:

Always double-check your substitution step by plugging the solution back into the original equations to verify!