Solve the system of equations. {:[6x-5y=-32],[-7x+8y=46],[x=◻],[y=◻]:}

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either 'x' or 'y'. For this problem, we will eliminate 'x' by finding a common multiple for the coefficients 6 and 7.Multiply Equations by Common Coefficients: Multiply the first equation by 7 and the second equation by 6 to obtain a common coefficient for 'x'. First equation: 7*(6x - 5y) = 7*(-32) gives us 42x - 35y = -224. Second equation: 6*(-7x + 8y) = 6*46 gives us -42x + 48y = 276.Add Equations to Eliminate Variable: Add the two new equations to eliminate 'x'. (42x - 35y) + (-42x + 48y) = -224 + 276 42x - 42x - 35y + 48y = 52 0x + 13y = 52Solve for y: Solve for 'y'. Divide both sides of the equation by 13 to isolate 'y'. 13y / 13 = 52 / 13 y = 4Substitute y into Equation: Substitute y = 4 into one of the original equations to solve for 'x'. We will use the first equation 6x - 5y = -32. 6x - 5(4) = -32 6x - 20 = -32Isolate x Term: Add 20 to both sides of the equation to isolate the term with 'x'. 6x - 20 + 20 = -32 + 20 6x = -12Solve for x: Divide both sides of the equation by 6 to solve for 'x'. 6x / 6 = -12 / 6 x = -2Write Solution as Coordinate Point: Write the solution as a coordinate point. The solution is (-2, 4).

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Solve the system of equations.

{:[6x-5y=-32],[-7x+8y=46],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 6 x-5 y=-32 \\ -7 x+8 y=46 \\ x=\square \\ y=\square \end{array}$

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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} 6 x-5 y=-32 \\ -7 x+8 y=46 \\ x=\square \\ y=\square \end{array}

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either ' $x$ ' or ' $y$ '. For this problem, we will eliminate ' $x$ ' by finding a common multiple for the coefficients $6$ and $7$ .
Multiply Equations by Common Coefficients: Multiply the first equation by $7$ and the second equation by $6$ to obtain a common coefficient for ' $x$ '. $\newline$ First equation: $7(6x - 5y) = 7(-32)$ gives us $42x - 35y = -224$ . $\newline$ Second equation: $6(-7x + 8y) = 6 imes 46$ gives us $-42x + 48y = 276$ .
Add Equations to Eliminate Variable: Add the two new equations to eliminate 'x'. $\newline$ $(42x - 35y) + (-42x + 48y) = -224 + 276$ $\newline$ $42x - 42x - 35y + 48y = 52$ $\newline$ $0x + 13y = 52$
Solve for y: Solve for 'y'. Divide both sides of the equation by $13$ to isolate 'y'. $\newline$ $\frac{13y}{13} = \frac{52}{13}$ $\newline$ $y = 4$
Substitute $y$ into Equation: Substitute $y = 4$ into one of the original equations to solve for ' $x$ '. We will use the first equation $6x - 5y = -32$ .
$6x - 5(4) = -32$
$6x - 20 = -32$
Isolate x Term: Add $20$ to both sides of the equation to isolate the term with 'x'. $\newline$ $6x - 20 + 20 = -32 + 20$ $\newline$ $6x = -12$
Solve for x: Divide both sides of the equation by $6$ to solve for 'x'. $\newline$ $\frac{6x}{6} = \frac{-12}{6}$ $\newline$ $x = -2$
Write Solution as Coordinate Point: Write the solution as a coordinate point. The solution is $(-2, 4)$ .