Solve the system of equations. {:[-4y+11 x-67=0],[2y+5x-19=0],[x=◻],[y=◻]:}

Write equations: Write down the system of equations. We have the following system of equations: -4y + 11x - 67 = 0 2y + 5x - 19 = 0Solve for y: Solve one of the equations for one of the variables. Let's solve the second equation for y: 2y = -5x + 19 y = (-5/2)x + 19/2Substitute y into first equation: Substitute the expression for y into the first equation. Substitute y = (-5/2)x + 19/2 into the first equation: -4((-5/2)x + 19/2) + 11x - 67 = 0Distribute and simplify: Distribute and simplify the first equation. -4 * (-5/2)x + -4 * (19/2) + 11x - 67 = 0 10x - 38 + 11x - 67 = 0 21x - 105 = 0Solve for x: Solve for x. 21x = 105 x = 105 / 21 x = 5Substitute x into y expression: Substitute x = 5 into the expression for y. y = (-5/2)(5) + 19/2 y = (-25/2) + 19/2Calculate y: Calculate the value of y. y = (-25/2) + 19/2 y = (-25 + 19) / 2 y = -6 / 2 y = -3Write solution as ordered pair: Write the solution as an ordered pair. The solution to the system of equations is (x, y) = (5, -3).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the system of equations.

{:[-4y+11 x-67=0],[2y+5x-19=0],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -4 y+11 x-67=0 \\ 2 y+5 x-19=0 \\ x=\square \\ y=\square \end{array}$

View step-by-step help

Home

Math Problems

Algebra 2

Solve a system of equations using elimination

Full solution

Q. Solve the system of equations.

\newline

\begin{array}{l} -4 y+11 x-67=0 \\ 2 y+5 x-19=0 \\ x=\square \\ y=\square \end{array}

Write equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $-4y + 11x - 67 = 0$ $\newline$ $2y + 5x - 19 = 0$
Solve for y: Solve one of the equations for one of the variables. $\newline$ Let's solve the second equation for y: $\newline$ $2y = -5x + 19$ $\newline$ $y = \frac{-5}{2}x + \frac{19}{2}$
Substitute $y$ into first equation: Substitute the expression for $y$ into the first equation. $\newline$ Substitute $y = \frac{-5}{2}x + \frac{19}{2}$ into the first equation: $\newline$ \(-4\left(\frac{ $-5$ }{ $2$ }x + \frac{ $19$ }{ $2$ }\right) + $11$ x - $67$ = $0$ ＂}
Distribute and simplify: Distribute and simplify the first equation. $\newline$ $-4 \cdot \left(-\frac{5}{2}\right)x + -4 \cdot \left(\frac{19}{2}\right) + 11x - 67 = 0$ $\newline$ $10x - 38 + 11x - 67 = 0$ $\newline$ $21x - 105 = 0$
Solve for x: Solve for x. $\newline$ $21x = 105$ $\newline$ $x = \frac{105}{21}$ $\newline$ $x = 5$
Substitute $x$ into $y$ expression: Substitute $x = 5$ into the expression for $y$ .
$y = \left(-\frac{5}{2}\right)(5) + \frac{19}{2}$
$y = \left(-\frac{25}{2}\right) + \frac{19}{2}$
Calculate y: Calculate the value of $y$ .
$y = \frac{-25}{2} + \frac{19}{2}$
$y = \frac{-25 + 19}{2}$
$y = \frac{-6}{2}$
$y = -3$
Write solution as ordered pair: Write the solution as an ordered pair. $\newline$ The solution to the system of equations is $(x, y) = (5, -3)$ .