Solve the system of equations. {:[-2x-7y=30],[7x+4y=18],[x=◻],[y=◻]:}

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either 'x' or 'y'. Let's eliminate 'x' by multiplying the first equation by 7 and the second equation by 2 to make the coefficients of 'x' opposites.Multiply First Equation by 7: Multiply the first equation by 7. 7(-2x - 7y) = 7(30) -14x - 49y = 210Multiply Second Equation by 2: Multiply the second equation by 2. 2(7x + 4y) = 2(18) 14x + 8y = 36Add Modified Equations to Eliminate 'x': Add the modified equations to eliminate 'x'. (-14x - 49y) + (14x + 8y) = 210 + 36 -14x + 14x - 49y + 8y = 246 -41y = 246Solve for 'y': Solve for 'y'. Divide both sides of the equation by -41 to find the value of 'y'. y = 246 / -41 y = -6Substitute 'y = -6' into Original Equation: Substitute y = -6 into one of the original equations to solve for 'x'. We'll use the second equation 7x + 4y = 18. 7x + 4(-6) = 18 7x - 24 = 18Solve for 'x': Solve for 'x'. Add 24 to both sides of the equation. 7x = 18 + 24 7x = 42 Divide both sides by 7. x = 42 / 7 x = 6

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Solve the system of equations.

{:[-2x-7y=30],[7x+4y=18],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -2 x-7 y=30 \\ 7 x+4 y=18 \\ x=\square \\ y=\square \end{array}$

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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} -2 x-7 y=30 \\ 7 x+4 y=18 \\ x=\square \\ y=\square \end{array}

Identify Variable to Eliminate: Identify the variable to eliminate. We can choose to eliminate either ' $x$ ' or ' $y$ '. Let's eliminate ' $x$ ' by multiplying the first equation by $7$ and the second equation by $2$ to make the coefficients of ' $x$ ' opposites.
Multiply First Equation by $7$ : Multiply the first equation by $7$ . $\newline$ $7(-2x - 7y) = 7(30)$ $\newline$ $-14x - 49y = 210$
Multiply Second Equation by $2$ : Multiply the second equation by $2$ . $\newline$ $2(7x + 4y) = 2(18)$ $\newline$ $14x + 8y = 36$
Add Modified Equations to Eliminate 'x': Add the modified equations to eliminate 'x'. $\newline$ $(-14x - 49y) + (14x + 8y) = 210 + 36$ $\newline$ $-14x + 14x - 49y + 8y = 246$ $\newline$ $-41y = 246$
Solve for 'y': Solve for 'y'. $\newline$ Divide both sides of the equation by $-41$ to find the value of 'y'. $\newline$ $y = \frac{246}{-41}$ $\newline$ $y = -6$
Substitute $y = -6$ into Original Equation: Substitute $y = -6$ into one of the original equations to solve for $x$ . We'll use the second equation $7x + 4y = 18$ .
$7x + 4(-6) = 18$
$7x - 24 = 18$
Solve for 'x': Solve for 'x'. $\newline$ Add $24$ to both sides of the equation. $\newline$ $7x = 18 + 24$ $\newline$ $7x = 42$ $\newline$ Divide both sides by $7$ . $\newline$ $x = \frac{42}{7}$ $\newline$ $x = 6$