Solve the system of equations. {:[13 x-6y=22],[x=y+6],[x=◻],[y=◻]:}

Identify Equations: Identify the given system of equations. We have the following system of equations: 1) 13x - 6y = 22 2) x = y + 6 We need to find the values of x and y that satisfy both equations.Substitute and Solve: Substitute the second equation into the first equation. Since x = y + 6, we can replace x in the first equation with y + 6 to solve for y. 13(y + 6) - 6y = 22Combine Terms: Distribute and combine like terms. 13y + 78 - 6y = 22 (13y - 6y) + 78 = 22 7y + 78 = 22Isolate Variable: Isolate the variable y. Subtract 78 from both sides of the equation to solve for y. 7y = 22 - 78 7y = -56Find Value of y: Divide both sides by 7 to find the value of y. y = -56 / 7 y = -8Substitute for x: Substitute the value of y back into the second equation to solve for x. x = y + 6 x = -8 + 6 x = -2Check Solution: Check the solution by substituting x and y into both original equations. First equation: 13x - 6y = 22 13(-2) - 6(-8) = 22 -26 + 48 = 22 22 = 22 (True) Second equation: x = y + 6 -2 = -8 + 6 -2 = -2 (True) Both equations are satisfied, so the solution is correct.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations.

{:[13 x-6y=22],[x=y+6],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 13 x-6 y=22 \\ x=y+6 \\ x=\square \\ y=\square \end{array}$

View step-by-step help

Home

Math Problems

Algebra 1

Solve a system of equations using substitution

Full solution

Q. Solve the system of equations.

\newline

\begin{array}{l} 13 x-6 y=22 \\ x=y+6 \\ x=\square \\ y=\square \end{array}

Identify Equations: Identify the given system of equations. $\newline$ We have the following system of equations: $\newline$ $1$ ) $13x - 6y = 22$ $\newline$ $2$ ) $x = y + 6$ $\newline$ We need to find the values of $x$ and $y$ that satisfy both equations.
Substitute and Solve: Substitute the second equation into the first equation. $\newline$ Since $x = y + 6$ , we can replace $x$ in the first equation with $y + 6$ to solve for $y$ . $\newline$ $13(y + 6) - 6y = 22$
Combine Terms: Distribute and combine like terms. $\newline$ $13y + 78 - 6y = 22$ $\newline$ $(13y - 6y) + 78 = 22$ $\newline$ $7y + 78 = 22$
Isolate Variable: Isolate the variable $y$ . $\newline$ Subtract $78$ from both sides of the equation to solve for $y$ . $\newline$ $7y = 22 - 78$ $\newline$ $7y = -56$
Find Value of y: Divide both sides by $7$ to find the value of $y$ . $y = \frac{-56}{7}$ $y = -8$
Substitute for x: Substitute the value of $y$ back into the second equation to solve for $x$ . $x = y + 6$ $x = -8 + 6$ $x = -2$
Check Solution: Check the solution by substituting $x$ and $y$ into both original equations. $\newline$ First equation: $13x - 6y = 22$ $\newline$ $13(-2) - 6(-8) = 22$ $\newline$ $-26 + 48 = 22$ $\newline$ $22 = 22$ (True) $\newline$ Second equation: $x = y + 6$ $\newline$ $-2 = -8 + 6$ $\newline$ $-2 = -2$ (True) $\newline$ Both equations are satisfied, so the solution is correct.