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

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:

$x + 8y = 16$

We can solve for $x$ as follows:

$x = 16 - 8y$

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

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

$-5(16 - 8y) + 9y = 18$

Simplify and solve for $y$:

- Distribute $-5$:

$-80 + 40y + 9y = 18$

- Combine like terms:

$49y - 80 = 18$

- Add 80 to both sides:

$49y = 98$

- Divide by 49:

$y = \frac{98}{49} = 2$

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

The expression for $x$ is:

$x = 16 - 8y$

- Substitute $y = 2$:

$x = 16 - 8(2)$ $x = 16 - 16$ $x = 0$

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