Question

solve the system of equations by substitution.\

$$\begin{cases}x = 4y + 10\\\\3x + 5y = -21\\end{cases}$$

\the solution of the system is x = \square and y = \square.\\(\text{type integers or simplified fractions.}\\)

Explanation:

Step1: Substitute x into second equation

Substitute $x=4y+10$ into $3x+5y=-21$:
$$3(4y+10)+5y=-21$$

Step2: Expand and simplify

Distribute 3, combine like terms:
$$12y+30+5y=-21$$
$$17y+30=-21$$

Step3: Solve for y

Isolate y, calculate value:
$$17y=-21-30$$
$$17y=-51$$
$$y=\frac{-51}{17}=-3$$

Step4: Solve for x

Substitute $y=-3$ into $x=4y+10$:
$$x=4(-3)+10$$
$$x=-12+10=-2$$

Answer:

$x=-2$ and $y=-3$