Solve the system by substitution. {:[y=-4x+5],[8x-2y=-42]:}

Substitute y in second equation: Substitute the expression for y from the first equation into the second equation. Given the first equation y = -4x + 5, we can substitute this into the second equation 8x - 2y = -42.Perform the substitution: Perform the substitution. 8x - 2(-4x + 5) = -42Distribute and simplify: Distribute the -2 across the parentheses. 8x + 8x - 10 = -42Combine like terms: Combine like terms. 16x - 10 = -42Isolate x term: Add 10 to both sides of the equation to isolate the term with x. 16x - 10 + 10 = -42 + 10 16x = -32Solve for x: Divide both sides by 16 to solve for x. 16x / 16 = -32 / 16 x = -2Substitute x back into first equation: Substitute the value of x back into the first equation to solve for y. y = -4(-2) + 5Perform multiplication and addition: Perform the multiplication and addition to find y. y = 8 + 5 y = 13Write solution as ordered pair: Write the solution as an ordered pair (x, y). The solution is (-2, 13).

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Solve the system by substitution.

{:[y=-4x+5],[8x-2y=-42]:}

Solve the system by substitution. $\newline$ $\begin{aligned} y & =-4 x+5 \\ 8 x-2 y & =-42 \end{aligned}$

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Algebra 2

Solve a system of equations in three variables using substitution

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Q. Solve the system by substitution.

\newline

\begin{aligned} y & =-4 x+5 \\ 8 x-2 y & =-42 \end{aligned}

Substitute $y$ in second equation: Substitute the expression for $y$ from the first equation into the second equation. $\newline$ Given the first equation $y = -4x + 5$ , we can substitute this into the second equation $8x - 2y = -42$ .
Perform the substitution: Perform the substitution. $8x - 2(-4x + 5) = -42$
Distribute and simplify: Distribute the $-2$ across the parentheses. $8x + 8x - 10 = -42$
Combine like terms: Combine like terms. $16x - 10 = -42$
Isolate x term: Add $10$ to both sides of the equation to isolate the term with $x$ . $\newline$ $16x - 10 + 10 = -42 + 10$ $\newline$ $16x = -32$
Solve for x: Divide both sides by $16$ to solve for x. $\newline$ $\frac{16x}{16} = \frac{-32}{16}$ $\newline$ $x = -2$
Substitute $x$ back into first equation: Substitute the value of $x$ back into the first equation to solve for $y$ . $y = -4(-2) + 5$
Perform multiplication and addition: Perform the multiplication and addition to find $y$ . $y = 8 + 5$ $y = 13$
Write solution as ordered pair: Write the solution as an ordered pair $(x, y)$ . $\newline$ The solution is $(-2, 13)$ .