Solve using substitution. –10x − 7y = –7 x = 7 (_____, _____)

Substitute x in first equation: Substitute the value of x into the first equation. Since we know that x = 7, we can substitute 7 in place of x in the equation –10x − 7y = –7. This gives us: –10(7) − 7y = –7.Simplify after substitution: Simplify the equation after substitution. Now we calculate –10 times 7, which is –70. So the equation becomes: –70 − 7y = –7.Isolate variable y: Isolate the variable y. To find the value of y, we need to isolate y on one side of the equation. We do this by adding 70 to both sides of the equation. This gives us: –70 + 70 − 7y = –7 + 70.Simplify after adding 70: Simplify the equation after adding 70 to both sides. The equation now simplifies to: –7y = 63.Solve for y: Solve for y. To solve for y, we divide both sides of the equation by –7. This gives us: y = 63 / (–7).Calculate y value: Calculate the value of y. Dividing 63 by –7 gives us y = –9.Write solution as ordered pair: Write the solution as an ordered pair. Since we have found the values of x and y, we can write the solution as an ordered pair (x, y). The final answer is (7, –9).

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Solve using substitution. $\newline$ $-10x - 7y = -7$ $\newline$ $x = 7$ $\newline$ (_, _)

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Precalculus

Solve a system of equations using substitution

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Q. Solve using substitution.

\newline

-10x - 7y = -7

\newline

x = 7

\newline

(_____, _____)

Substitute $x$ in first equation: Substitute the value of $x$ into the first equation. $\newline$ Since we know that $x = 7$ , we can substitute $7$ in place of $x$ in the equation $–10x − 7y = –7$ . $\newline$ This gives us: $–10(7) − 7y = –7$ .
Simplify after substitution: Simplify the equation after substitution. $\newline$ Now we calculate $-10 \times 7$ , which is $-70$ . $\newline$ So the equation becomes: $-70 - 7y = -7$ .
Isolate variable y: Isolate the variable y. $\newline$ To find the value of y, we need to isolate y on one side of the equation. We do this by adding $70$ to both sides of the equation. $\newline$ This gives us: $-70 + 70 - 7y = -7 + 70$ .
Simplify after adding $70$ : Simplify the equation after adding $70$ to both sides. $\newline$ The equation now simplifies to: $-7y = 63$ .
Solve for y: Solve for y. $\newline$ To solve for y, we divide both sides of the equation by $–7$ . $\newline$ This gives us: $y = \frac{63}{(–7)}$ .
Calculate y value: Calculate the value of y. $\newline$ Dividing $63$ by $-7$ gives us $y = -9$ .
Write solution as ordered pair: Write the solution as an ordered pair. $\newline$ Since we have found the values of $x$ and $y$ , we can write the solution as an ordered pair $(x, y)$ . $\newline$ The final answer is $(7, -9)$ .