Solve the system of equations. {:[5x-4y=-10],[y=2x-5],[x=◻],[y=◻]:}

Write Equations: Write down the given system of equations. We have the following system of equations: 5x - 4y = -10 y = 2x - 5 We need to find the values of x and y that satisfy both equations.Substitute and Simplify: Substitute the second equation into the first equation. Since y = 2x - 5, we can replace y in the first equation with 2x - 5: 5x - 4(2x - 5) = -10 Now we will solve for x.Distribute and Combine: Distribute the -4 across the terms in the parentheses and simplify. 5x - 4(2x) + 4(5) = -10 5x - 8x + 20 = -10 Combine like terms: -3x + 20 = -10Solve for x: Solve for x. Subtract 20 from both sides of the equation: -3x + 20 - 20 = -10 - 20 -3x = -30 Divide both sides by -3: x = -30 / -3 x = 10Substitute for y: Substitute the value of x back into the second equation to solve for y. We know that y = 2x - 5, so: y = 2(10) - 5 y = 20 - 5 y = 15

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Solve the system of equations.

{:[5x-4y=-10],[y=2x-5],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 5 x-4 y=-10 \\ y=2 x-5 \\ x=\square \\ y=\square \end{array}$

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Algebra 1

Solve a system of equations using substitution

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Q. Solve the system of equations.

\newline

\begin{array}{l} 5 x-4 y=-10 \\ y=2 x-5 \\ x=\square \\ y=\square \end{array}

Write Equations: Write down the given system of equations. $\newline$ We have the following system of equations: $\newline$ $5x - 4y = -10$ $\newline$ $y = 2x - 5$ $\newline$ We need to find the values of $x$ and $y$ that satisfy both equations.
Substitute and Simplify: Substitute the second equation into the first equation. $\newline$ Since $y = 2x - 5$ , we can replace $y$ in the first equation with $2x - 5$ : $\newline$ $5x - 4(2x - 5) = -10$ $\newline$ Now we will solve for $x$ .
Distribute and Combine: Distribute the $-4$ across the terms in the parentheses and simplify. $5x - 4(2x) + 4(5) = -10$ $5x - 8x + 20 = -10$ Combine like terms: $-3x + 20 = -10$
Solve for x: Solve for x. $\newline$ Subtract $20$ from both sides of the equation: $\newline$ $-3x + 20 - 20 = -10 - 20$ $\newline$ $-3x = -30$ $\newline$ Divide both sides by $-3$ : $\newline$ $x = \frac{-30}{-3}$ $\newline$ $x = 10$
Substitute for $y$ : Substitute the value of $x$ back into the second equation to solve for $y$ . $\newline$ We know that $y = 2x - 5$ , so: $\newline$ $y = 2(10) - 5$ $\newline$ $y = 20 - 5$ $\newline$ $y = 15$