Solve the system of equations. {:[5x-7y=58],[y=-x+2],[x=◻],[y=◻]:}

Substitute y into first equation: Substitute y from the second equation into the first equation. We have y = -x + 2. Substitute this into 5x - 7y = 58. 5x - 7(-x + 2) = 58Distribute and simplify: Distribute the -7 across the terms in the parentheses and simplify. 5x + 7x - 14 = 58 12x - 14 = 58Isolate the term with x: Add 14 to both sides to isolate the term with the variable x. 12x - 14 + 14 = 58 + 14 12x = 72Solve for x: Divide both sides by 12 to solve for x. 12x / 12 = 72 / 12 x = 6Substitute x back into second equation: Substitute x back into the second equation to solve for y. y = -x + 2 y = -6 + 2 y = -4Write the solution as an ordered pair: Write the solution as an ordered pair. The solution is (x, y) = (6, -4).

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Solve the system of equations.

{:[5x-7y=58],[y=-x+2],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 5 x-7 y=58 \\ y=-x+2 \\ x=\square \\ y=\square \end{array}$

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Algebra 1

Solve a system of equations using substitution

Full solution

Q. Solve the system of equations.

\newline

\begin{array}{l} 5 x-7 y=58 \\ y=-x+2 \\ x=\square \\ y=\square \end{array}

Substitute $y$ into first equation: Substitute $y$ from the second equation into the first equation. $\newline$ We have $y = -x + 2$ . Substitute this into $5x - 7y = 58$ . $\newline$ $5x - 7(-x + 2) = 58$
Distribute and simplify: Distribute the $-7$ across the terms in the parentheses and simplify. $5x + 7x - 14 = 58$ $12x - 14 = 58$
Isolate the term with x: Add $14$ to both sides to isolate the term with the variable $x$ . $\newline$ $12$ x - $14$ + $14$ = $58$ + $14$ $\newline$ $12$ x = $72$
Solve for x: Divide both sides by $12$ to solve for x. $\newline$ $\frac{12x}{12} = \frac{72}{12}$ $\newline$ $x = 6$
Substitute $x$ back into second equation: Substitute $x$ back into the second equation to solve for $y$ .
$y = -x + 2$
$y = -6 + 2$
$y = -4$
Write the solution as an ordered pair: Write the solution as an ordered pair. $\newline$ The solution is $(x, y) = (6, -4)$ .