Solve the system of equations. {:[-9y+4x-11=0],[-3y+10 x+31=0],[x=◻],[y=◻]:}

Write equations: Write down the system of equations. -9y + 4x - 11 = 0 -3y + 10x + 31 = 0 We need to find the values of x and y that satisfy both equations.Rearrange first equation: Rearrange the first equation to express x in terms of y. 4x = 9y + 11 x = (9y + 11) / 4 This equation now expresses x in terms of y.Substitute expression for x: Substitute the expression for x from Step 2 into the second equation. -3y + 10((9y + 11) / 4) + 31 = 0 This will allow us to solve for y.Distribute and simplify: Distribute and simplify the equation from Step 3. -3y + (90y + 110) / 4 + 31 = 0 Multiply everything by 4 to clear the fraction: -12y + 90y + 110 + 124 = 0 This simplifies to: 78y + 234 = 0Solve for y: Solve for y. 78y = -234 y = -234 / 78 y = -3 We have found the value of y.Substitute y into expression for x: Substitute y = -3 into the expression for x from Step 2. x = (9(-3) + 11) / 4 x = (-27 + 11) / 4 x = -16 / 4 x = -4 We have found the value of x.Check the solution: Check the solution by substituting x and y into both original equations. First equation: -9(-3) + 4(-4) - 11 = 0 27 - 16 - 11 = 0 0 = 0 Second equation: -3(-3) + 10(-4) + 31 = 0 9 - 40 + 31 = 0 0 = 0 Both checks are correct.

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Solve the system of equations.

{:[-9y+4x-11=0],[-3y+10 x+31=0],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -9 y+4 x-11=0 \\ -3 y+10 x+31=0 \\ x=\square \\ y=\square \end{array}$

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Algebra 2

Solve a system of equations using elimination

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Q. Solve the system of equations.

\newline

\begin{array}{l} -9 y+4 x-11=0 \\ -3 y+10 x+31=0 \\ x=\square \\ y=\square \end{array}

Write equations: Write down the system of equations. $\newline$ $-9y + 4x - 11 = 0$ $\newline$ $-3y + 10x + 31 = 0$ $\newline$ We need to find the values of $x$ and $y$ that satisfy both equations.
Rearrange first equation: Rearrange the first equation to express $x$ in terms of $y$ .
$4x = 9y + 11$
$x = \frac{9y + 11}{4}$
This equation now expresses $x$ in terms of $y$ .
Substitute expression for x: Substitute the expression for $x$ from Step $2$ into the second equation. $-3y + 10\left(\frac{9y + 11}{4}\right) + 31 = 0$ This will allow us to solve for $y$ .
Distribute and simplify: Distribute and simplify the equation from Step $3$ . $\newline$ $-3y + \frac{90y + 110}{4} + 31 = 0$ $\newline$ Multiply everything by $4$ to clear the fraction: $\newline$ $-12y + 90y + 110 + 124 = 0$ $\newline$ This simplifies to: $\newline$ $78y + 234 = 0$
Solve for y: Solve for y. $\newline$ $78y = -234$ $\newline$ $y = \frac{-234}{78}$ $\newline$ $y = -3$ $\newline$ We have found the value of $y$ .
Substitute $y$ into expression for $x$ : Substitute $y = -3$ into the expression for $x$ from Step $2$ . $\newline$ $x = \frac{9(-3) + 11}{4}$ $\newline$ $x = \frac{-27 + 11}{4}$ $\newline$ $x = \frac{-16}{4}$ $\newline$ $x = -4$ $\newline$ We have found the value of $x$ .
Check the solution: Check the solution by substituting $x$ and $y$ into both original equations. $\newline$ First equation: $-9(-3) + 4(-4) - 11 = 0$ $\newline$ $27 - 16 - 11 = 0$ $\newline$ $0 = 0$ $\newline$ Second equation: $-3(-3) + 10(-4) + 31 = 0$ $\newline$ $9 - 40 + 31 = 0$ $\newline$ $0 = 0$ $\newline$ Both checks are correct.