Question

solve the system of linear equations by substitution.\\(-5x + 3y = 51\\)\\(y = 10x - 8\\)

Explanation:

Step1: Substitute $y$ into first equation

$$\begin{align*} -5x + 3(10x - 8) &= 51 \end{align*}$$

Step2: Expand and simplify the equation

$$\begin{align*} -5x + 30x - 24 &= 51 \\ 25x - 24 &= 51 \end{align*}$$

Step3: Isolate the $x$-term

$$\begin{align*} 25x &= 51 + 24 \\ 25x &= 75 \end{align*}$$

Step4: Solve for $x$

$$\begin{align*} x &= \frac{75}{25} \\ x &= 2 \end{align*}$$

Step5: Substitute $x$ into $y$-equation

$$\begin{align*} y &= 10(2) - 8 \end{align*}$$

Step6: Calculate the value of $y$

$$\begin{align*} y &= 20 - 8 \\ y &= 12 \end{align*}$$

Answer:

$x=2$, $y=12$