Solve the system of equations. {:[-5y+8x=-18],[5y+2x=58],[x=◻],[y=◻]:}

Write Equations: Write down the system of equations. We have the following system of equations: -5y + 8x = -18 5y + 2x = 58 We need to find the values of x and y that satisfy both equations.Add Equations: Add the two equations together to eliminate y. By adding the two equations, we get: (-5y + 8x) + (5y + 2x) = -18 + 58 This simplifies to: 8x + 2x = 40Combine & Solve for x: Combine like terms and solve for x. 8x + 2x = 40 10x = 40 Now, divide both sides by 10 to solve for x: x = 40 / 10 x = 4Substitute & Solve for y: Substitute the value of x into one of the original equations to solve for y. We can use the second equation for this purpose: 5y + 2x = 58 Substitute x = 4 into the equation: 5y + 2(4) = 58 5y + 8 = 58Final Solution: Subtract 8 from both sides to isolate the term with y. 5y + 8 - 8 = 58 - 8 5y = 50 Now, divide both sides by 5 to solve for y: y = 50 / 5 y = 10

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Solve the system of equations.

{:[-5y+8x=-18],[5y+2x=58],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -5 y+8 x=-18 \\ 5 y+2 x=58 \\ x=\square \\ y=\square \end{array}$

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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} -5 y+8 x=-18 \\ 5 y+2 x=58 \\ x=\square \\ y=\square \end{array}

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $-5y + 8x = -18$ $\newline$ $5y + 2x = 58$ $\newline$ We need to find the values of $x$ and $y$ that satisfy both equations.
Add Equations: Add the two equations together to eliminate $y$ . $\newline$ By adding the two equations, we get: $\newline$ $(-5y + 8x) + (5y + 2x) = -18 + 58$ $\newline$ This simplifies to: $\newline$ $8x + 2x = 40$
Combine & Solve for x: Combine like terms and solve for x. $\newline$ $8x + 2x = 40$ $\newline$ $10x = 40$ $\newline$ Now, divide both sides by $10$ to solve for x: $\newline$ $x = \frac{40}{10}$ $\newline$ $x = 4$
Substitute & Solve for y: Substitute the value of $x$ into one of the original equations to solve for $y$ . We can use the second equation for this purpose: $5y + 2x = 58$ Substitute $x = 4$ into the equation: $5y + 2(4) = 58$ $5y + 8 = 58$
Final Solution: Subtract $8$ from both sides to isolate the term with $y$ . $\newline$ $5y + 8 - 8 = 58 - 8$ $\newline$ $5y = 50$ $\newline$ Now, divide both sides by $5$ to solve for $y$ : $\newline$ $y = \frac{50}{5}$ $\newline$ $y = 10$