Solve by the elimination method. {:[9x-6y=19],[-6x+4y=11]:}

Write Equations: Write down the system of equations to be solved. {:[9x-6y=19],[-6x+4y=11]:}Multiply Second Equation: Multiply the second equation by a number that will allow us to eliminate one of the variables when we add the two equations together. In this case, we can multiply the second equation by 1.5 to make the coefficient of x in the second equation equal to the negative of the coefficient of x in the first equation. 1.5(-6x + 4y) = 1.5(11) This gives us: -9x + 6y = 16.5Add Equations: Add the modified second equation to the first equation to eliminate the x variable. (9x - 6y) + (-9x + 6y) = 19 + 16.5 This simplifies to: 0x + 0y = 35.5

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Math Problems

Grade 8

Write an equation word problem

Full solution

Q. Solve by the elimination method.

\newline

\begin{array}{r} 9 x-6 y=19 \\ -6 x+4 y=11 \end{array}

Write Equations: Write down the system of equations to be solved. $\begin{cases} 9x-6y=19 \ -6x+4y=11 \end{cases}$
Multiply Second Equation: Multiply the second equation by a number that will allow us to eliminate one of the variables when we add the two equations together. In this case, we can multiply the second equation by $1.5$ to make the coefficient of $x$ in the second equation equal to the negative of the coefficient of $x$ in the first equation. $\newline$ $1.5(-6x + 4y) = 1.5(11)$ $\newline$ This gives us: $\newline$ $-9x + 6y = 16.5$
Add Equations: Add the modified second equation to the first equation to eliminate the $x$ variable. $\newline$ $(9x - 6y) + (-9x + 6y) = 19 + 16.5$ $\newline$ This simplifies to: $\newline$ $0x + 0y = 35.5$