Solve the system of equations. {:[3y+10 x-54=0],[5y-2x-34=0],[x=◻],[y=◻]:}

Rearrange to solve for y: First, let's rearrange the first equation to solve for y. 3y = 54 - 10x y = (54 - 10x) / 3 y = 18 - (10/3)xSubstitute y in second equation: Now, substitute y in the second equation with the expression we found. 5(18 - (10/3)x) - 2x = 34Distribute and simplify: Distribute the 5 into the parentheses. 90 - (50/3)x - 2x = 34Combine like terms: Combine like terms by finding a common denominator for x. (90 - (50/3)x - (6/3)x = 34) 90 - (56/3)x = 34Isolate x terms: Subtract 90 from both sides to isolate the x terms. - (56/3)x = 34 - 90 - (56/3)x = -56Solve for x: Multiply both sides by -3/56 to solve for x. x = (-56 * -3/56) x = 3Substitute x back into y equation: Now, substitute x back into the equation we found for y. y = 18 - (10/3)(3)Simplify y equation: Simplify the equation for y. y = 18 - 10 y = 8

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Solve the system of equations.

{:[3y+10 x-54=0],[5y-2x-34=0],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 3 y+10 x-54=0 \\ 5 y-2 x-34=0 \\ x=\square \\ y=\square \end{array}$

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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} 3 y+10 x-54=0 \\ 5 y-2 x-34=0 \\ x=\square \\ y=\square \end{array}

Rearrange to solve for y: First, let's rearrange the first equation to solve for y. $\newline$ $3y = 54 - 10x$ $\newline$ $y = \frac{54 - 10x}{3}$ $\newline$ $y = 18 - \frac{10}{3}x$
Substitute $y$ in second equation: Now, substitute $y$ in the second equation with the expression we found. $5(18 - (\frac{10}{3})x) - 2x = 34$
Distribute and simplify: Distribute the $5$ into the parentheses. $90 - \left(\frac{50}{3}\right)x - 2x = 34$
Combine like terms: Combine like terms by finding a common denominator for $x$ . $\$90 - \frac{50}{3}x - \frac{6}{3}x = 34$ \) $90 - \frac{56}{3}x = 34$
Isolate x terms: Subtract $90$ from both sides to isolate the x terms. $\newline$ $-(\frac{56}{3})x = 34 - 90$ $\newline$ $-(\frac{56}{3})x = -56$
Solve for x: Multiply both sides by $-\frac{3}{56}$ to solve for x. $\newline$ $x = (-56 \times -\frac{3}{56})$ $\newline$ $x = 3$
Substitute $x$ back into $y$ equation: Now, substitute $x$ back into the equation we found for $y$ . $y = 18 - \left(\frac{10}{3}\right)(3)$
Simplify y equation: Simplify the equation for $y$ . $y = 18 - 10$ $y = 8$