Solve the system of equations. {:[7y+10 x-8=0],[2y-5x-18=0],[x=◻],[y=◻]:}

Write equations: Write down the system of equations. We have the following system of equations: 7y + 10x - 8 = 0 2y - 5x - 18 = 0Solve for y: Solve one of the equations for one variable. Let's solve the first equation for y: 7y = -10x + 8 y = (-10x + 8) / 7Substitute y into second equation: Substitute the expression for y into the second equation. Substitute y = (-10x + 8) / 7 into 2y - 5x - 18 = 0: 2((-10x + 8) / 7) - 5x - 18 = 0Clear the fraction: Multiply through by 7 to clear the fraction. 14(-10x + 8) - 35x - 126 = 0Combine like terms: Distribute and combine like terms. -140x + 112 - 35x - 126 = 0 -175x - 14 = 0Solve for x: Solve for x. -175x = 14 x = 14 / -175 x = -2 / 25Substitute x into y expression: Substitute x back into the expression for y. y = (-10(-2 / 25) + 8) / 7 y = (20 / 25 + 8) / 7Simplify y expression: Simplify the expression for y. y = (4/5 + 8) / 7 y = (4/5 + 40/5) / 7 y = 44/5 / 7 y = 44/35Write the solution: Write the solution as an ordered pair. The solution is (x, y) = (-2/25, 44/35).

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Solve the system of equations.

{:[7y+10 x-8=0],[2y-5x-18=0],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} 7 y+10 x-8=0 \\ 2 y-5 x-18=0 \\ x=\square \\ y=\square \end{array}$

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Math Problems

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-8=0 \\ 2 y-5 x-18=0 \\ x=\square \\ y=\square \end{array}

Write equations: Write down the system of equations. $\newline$ We have the following system of equations: $\newline$ $7y + 10x - 8 = 0$ $\newline$ $2y - 5x - 18 = 0$
Solve for y: Solve one of the equations for one variable. $\newline$ Let's solve the first equation for y: $\newline$ $7y = -10x + 8$ $\newline$ $y = \frac{-10x + 8}{7}$
Substitute $y$ into second equation: Substitute the expression for $y$ into the second equation. $\newline$ Substitute $y = \frac{-10x + 8}{7}$ into $2y - 5x - 18 = 0$ : $\newline$ $2\left(\frac{-10x + 8}{7}\right) - 5x - 18 = 0$
Clear the fraction: Multiply through by $7$ to clear the fraction. $\newline$ $14(-10x + 8) - 35x - 126 = 0$
Combine like terms: Distribute and combine like terms. $\newline$ $-140x + 112 - 35x - 126 = 0$ $\newline$ $-175x - 14 = 0$
Solve for x: Solve for x. $\newline$ $-175x = 14$ $\newline$ $x = \frac{14}{-175}$ $\newline$ $x = -\frac{2}{25}$
Substitute $x$ into $y$ expression: Substitute $x$ back into the expression for $y$ .
$y = \frac{-10\left(\frac{-2}{25}\right) + 8}{7}$
$y = \frac{\frac{20}{25} + 8}{7}$
Simplify y expression: Simplify the expression for y. $\newline$ $y = \frac{4}{5} + 8 \div 7$ $\newline$ $y = \frac{4}{5} + \frac{40}{5} \div 7$ $\newline$ $y = \frac{44}{5} \div 7$ $\newline$ $y = \frac{44}{35}$
Write the solution: Write the solution as an ordered pair. $\newline$ The solution is $(x, y) = (-\frac{2}{25}, \frac{44}{35})$ .