Question

Substitution method 3x - 6y = 5 2x - 6y = 0

Answer 1

Answer: The solution to the system of equations is $\(x = 5\) and \(y = \frac{5}{3}\)$.

Step-by-step explanation:

To solve the system of equations using the substitution method, we first solve one of the equations for one variable and then substitute that expression into the other equation. Let's solve the second equation for x:

Given:

1) $\(3x - 6y = 5\)$

2) $\(2x - 6y = 0\)$

From equation 2, we can solve for x:

$\[2x - 6y = 0\]\[2x = 6y\]\[x = 3y\]$

Now, we substitute $\(x = 3y\)$ into equation 1:

$\[3(3y) - 6y = 5\]\[9y - 6y = 5\]\[3y = 5\]\[y = \frac{5}{3}\]$

Now that we have found the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use equation 2:

$\[2x - 6\left(\frac{5}{3}\right) = 0\]\[2x - 10 = 0\]\[2x = 10\]\[x = 5\]$

So, the solution to the system of equations is $\(x = 5\) and \(y = \frac{5}{3}\)$.