Solve the system of equations. {:[2x-9y=14],[x=-6y+7],[x=◻],[y=◻]:}

Solve second equation for x: Solve the second equation for x. The second equation is x = -6y + 7. We can use this equation to substitute for x in the first equation.Substitute x into first equation: Substitute x = -6y + 7 into the first equation. The first equation is 2x - 9y = 14. Substituting x gives us: 2(-6y + 7) - 9y = 14Distribute and combine like terms: Distribute and combine like terms. 2(-6y) + 2(7) - 9y = 14 -12y + 14 - 9y = 14 -21y + 14 = 14Isolate the variable y: Isolate the variable y. Subtract 14 from both sides of the equation: -21y + 14 - 14 = 14 - 14 -21y = 0Solve for y: Solve for y. Divide both sides by -21: y = 0 / -21 y = 0Substitute y into second equation: Substitute y = 0 into the second equation to find x. The second equation is x = -6y + 7. Substituting y = 0 gives us: x = -6(0) + 7 x = 0 + 7 x = 7Write the solution as an ordered pair: Write the solution as an ordered pair. The solution to the system of equations is (x, y) = (7, 0).

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Solve the system of equations.

{:[2x-9y=14],[x=-6y+7],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 2 x-9 y=14 \\ x=-6 y+7 \\ x=\square \\ y=\square \end{array}$

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Algebra 1

Solve a system of equations using substitution

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Q. Solve the system of equations.

\newline

\begin{array}{l} 2 x-9 y=14 \\ x=-6 y+7 \\ x=\square \\ y=\square \end{array}

Solve second equation for x: Solve the second equation for x. $\newline$ The second equation is $x = -6y + 7$ . We can use this equation to substitute for $x$ in the first equation.
Substitute $x$ into first equation: Substitute $x = -6y + 7$ into the first equation. $\newline$ The first equation is $2x - 9y = 14$ . Substituting $x$ gives us: $\newline$ $2(-6y + 7) - 9y = 14$
Distribute and combine like terms: Distribute and combine like terms. $\newline$ $2(-6y) + 2(7) - 9y = 14$ $\newline$ $-12y + 14 - 9y = 14$ $\newline$ $-21y + 14 = 14$
Isolate the variable y: Isolate the variable y. $\newline$ Subtract $14$ from both sides of the equation: $\newline$ $-21y + 14 - 14 = 14 - 14$ $\newline$ $-21y = 0$
Solve for y: Solve for y. $\newline$ Divide both sides by $-21$ : $\newline$ $y = \frac{0}{-21}$ $\newline$ $y = 0$
Substitute $y$ into second equation: Substitute $y = 0$ into the second equation to find $x$ . $\newline$ The second equation is $x = -6y + 7$ . Substituting $y = 0$ gives us: $\newline$ $x = -6(0) + 7$ $\newline$ $x = 0 + 7$ $\newline$ $x = 7$
Write the solution as an ordered pair: Write the solution as an ordered pair. $\newline$ The solution to the system of equations is $(x, y) = (7, 0)$ .