Solve the System of Equations: -5x+9y=18 and x+8y=16 Using Substitution

Find the value of x and and band the substitution method.

$\begin{cases} -5x+9y=18 \\ x+8y=16 \end{cases}$

To solve the given system of linear equations using the substitution method, follow these steps:

• Step 1: Solve the second equation for $x$.

From the second equation:

We can solve for $x$ as follows:

• Step 2: Substitute the expression for $x$ into the first equation.

Substitute $x = 16 - 8y$ into the first equation:

Simplify and solve for $y$:

- Distribute $-5$:

- Combine like terms:

- Add 80 to both sides:

- Divide by 49:

• Step 3: Substitute $y = 2$ back into the expression for $x$.

The expression for $x$ is:

- Substitute $y = 2$:

Therefore, the values that satisfy both equations in the system are $x = 0$ and $y = 2$.