Solve the system of equations. {:[-4x+7y=20],[y=3x+15],[x=◻],[y=◻]:}

Write Equations: Write down the system of equations. We have the following system of equations: -4x + 7y = 20 y = 3x + 15 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 = 3x + 15, we can replace y in the first equation with 3x + 15: -4x + 7(3x + 15) = 20Combine Terms: Distribute and combine like terms. -4x + 21x + 105 = 20 17x + 105 = 20Subtract and Solve: Subtract 105 from both sides of the equation. 17x = 20 - 105 17x = -85Divide to Find x: Divide both sides by 17 to solve for x. x = -85 / 17 x = -5Substitute for y: Substitute x back into the second equation to solve for y. y = 3(-5) + 15 y = -15 + 15 y = 0Final Solution: Write down the solution to the system of equations. The solution is x = -5 and y = 0.

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Solve the system of equations.

{:[-4x+7y=20],[y=3x+15],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -4 x+7 y=20 \\ y=3 x+15 \\ x=\square \\ y=\square \end{array}$

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Math Problems

Algebra 1

Solve a system of equations using substitution

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Q. Solve the system of equations.

\newline

\begin{array}{l} -4 x+7 y=20 \\ y=3 x+15 \\ x=\square \\ y=\square \end{array}

Write Equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $-4x + 7y = 20$ $\newline$ $y = 3x + 15$ $\newline$ 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 $y = 3x + 15$ , we can replace $y$ in the first equation with $3x + 15$ : $\newline$ $-4x + 7(3x + 15) = 20$
Combine Terms: Distribute and combine like terms. $\newline$ $-4x + 21x + 105 = 20$ $\newline$ $17x + 105 = 20$
Subtract and Solve: Subtract $105$ from both sides of the equation. $\newline$ $17x = 20 - 105$ $\newline$ $17x = -85$
Divide to Find x: Divide both sides by $17$ to solve for x. $\newline$ $x = \frac{-85}{17}$ $\newline$ $x = -5$
Substitute for y: Substitute $x$ back into the second equation to solve for $y$ . $y = 3(-5) + 15$ $y = -15 + 15$ $y = 0$
Final Solution: Write down the solution to the system of equations. $\newline$ The solution is $x = -5$ and $y = 0$ .