Solve the system of equations. {:[-4x+3y=-2],[y=x-1],[x=◻],[y=◻]:}

Identify Equations: Identify the given system of equations. We have a system of three equations: 1) -4x + 3y = -2 2) y = x - 1 3) x = ◻ 4) y = ◻ We need to find the values of x and y that satisfy all three equations.Substitute and Simplify: Substitute the second equation into the first equation. Since y = x - 1, we can replace y in the first equation with x - 1: -4x + 3(x - 1) = -2Solve for x: Simplify the equation and solve for x. -4x + 3x - 3 = -2 Combine like terms: -x - 3 = -2 Add 3 to both sides: -x = 1 Multiply both sides by -1 to solve for x: x = -1Substitute for y: Substitute the value of x into the second equation to find y. Since y = x - 1, we substitute x = -1: y = -1 - 1 y = -2Verify Solution: Verify the solution with the original system of equations. We need to check if x = -1 and y = -2 satisfy all three equations. For the first equation: -4(-1) + 3(-2) = -2 4 - 6 = -2 -2 = -2 (True) For the second equation: y = x - 1 -2 = -1 - 1 -2 = -2 (True) Since the third and fourth equations are placeholders for the solutions, we have found the correct values for x and y.

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Solve the system of equations.

{:[-4x+3y=-2],[y=x-1],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -4 x+3 y=-2 \\ y=x-1 \\ x=\square \\ y=\square \end{array}$

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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} -4 x+3 y=-2 \\ y=x-1 \\ x=\square \\ y=\square \end{array}

Identify Equations: Identify the given system of equations. $\newline$ We have a system of three equations: $\newline$ $1$ ) $-4x + 3y = -2$ $\newline$ $2$ ) $y = x - 1$ $\newline$ $3$ ) $x = \square$ $\newline$ $4$ ) $y = \square$ $\newline$ We need to find the values of $x$ and $y$ that satisfy all three equations.
Substitute and Simplify: Substitute the second equation into the first equation. $\newline$ Since $y = x - 1$ , we can replace $y$ in the first equation with $x - 1$ : $\newline$ $-4x + 3(x - 1) = -2$
Solve for x: Simplify the equation and solve for x. $\newline$ $-4x + 3x - 3 = -2$ $\newline$ Combine like terms: $\newline$ $-x - 3 = -2$ $\newline$ Add $3$ to both sides: $\newline$ $-x = 1$ $\newline$ Multiply both sides by $-1$ to solve for x: $\newline$ $x = -1$
Substitute for $y$ : Substitute the value of $x$ into the second equation to find $y$ . $\newline$ Since $y = x - 1$ , we substitute $x = -1$ : $\newline$ $y = -1 - 1$ $\newline$ $y = -2$
Verify Solution: Verify the solution with the original system of equations. $\newline$ We need to check if $x = -1$ and $y = -2$ satisfy all three equations. $\newline$ For the first equation: $\newline$ $-4(-1) + 3(-2) = -2$ $\newline$ $4 - 6 = -2$ $\newline$ $-2 = -2$ (True) $\newline$ For the second equation: $\newline$ $y = x - 1$ $\newline$ $-2 = -1 - 1$ $\newline$ $-2 = -2$ (True) $\newline$ Since the third and fourth equations are placeholders for the solutions, we have found the correct values for $x$ and $y$ .