Solve the system of equations. {:[7y+10 x=-11],[4y-3x=-15],[x=◻],[y=◻]:}

Write equations: Write down the system of equations to be solved. 7y + 10x = -11 4y - 3x = -15Multiply equations: Multiply the first equation by 3 and the second equation by 10 to make the coefficients of x in both equations the same (but opposite in sign). (3)(7y + 10x) = (3)(-11) (10)(4y - 3x) = (10)(-15) This gives us: 21y + 30x = -33 40y - 30x = -150Eliminate x: Add the two new equations together to eliminate x. (21y + 30x) + (40y - 30x) = -33 + (-150) This simplifies to: 61y = -183Solve for y: Solve for y by dividing both sides of the equation by 61. y = -183 / 61 y = -3Substitute y into equation: Substitute y = -3 into one of the original equations to solve for x. We'll use the first equation. 7(-3) + 10x = -11 -21 + 10x = -11Isolate x: Add 21 to both sides of the equation to isolate the term with x. 10x = -11 + 21 10x = 10Solve for x: Divide both sides of the equation by 10 to solve for x. x = 10 / 10 x = 1

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Solve the system of equations.

{:[7y+10 x=-11],[4y-3x=-15],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 7 y+10 x=-11 \\ 4 y-3 x=-15 \\ x=\square \\ y=\square \end{array}$

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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} 7 y+10 x=-11 \\ 4 y-3 x=-15 \\ x=\square \\ y=\square \end{array}

Write equations: Write down the system of equations to be solved. $\newline$ $7y + 10x = -11$ $\newline$ $4y - 3x = -15$
Multiply equations: Multiply the first equation by $3$ and the second equation by $10$ to make the coefficients of $x$ in both equations the same (but opposite in sign). $\newline$ $(3)(7y + 10x) = (3)(-11)$ $\newline$ $(10)(4y - 3x) = (10)(-15)$ $\newline$ This gives us: $\newline$ $21y + 30x = -33$ $\newline$ $40y - 30x = -150$
Eliminate $x$ : Add the two new equations together to eliminate $x$ .
$(21y + 30x) + (40y - 30x) = -33 + (-150)$
This simplifies to:
$61y = -183$
Solve for $y$ : Solve for $y$ by dividing both sides of the equation by $61$ . $y = \frac{-183}{61}$ $y = -3$
Substitute $y$ into equation: Substitute $y = -3$ into one of the original equations to solve for $x$ . We'll use the first equation. $7(-3) + 10x = -11$ $-21 + 10x = -11$
Isolate $x$ : Add $21$ to both sides of the equation to isolate the term with $x$ . $10x = -11 + 21$ $10x = 10$
Solve for x: Divide both sides of the equation by $10$ to solve for x. $\newline$ $x = \frac{10}{10}$ $\newline$ $x = 1$