How do you solve the system of equations 4y = 9x - 17 and 9x - 6y = 3?

1 Answer
Mar 24, 2018

$x = 5 \mathmr{and} y = 7$

Explanation:

Both equations have the same term in $x$.

To eliminate the $x$ term, you could subtract the equations,
However, here is another option:

Isolate the $9 x$ term in each equation.

color(blue)(9x = 6y+3)" " and" "color(red)(9x =4y+17

$\textcolor{w h i t e}{w w w w w w w w w .} \textcolor{b l u e}{9 x} = \textcolor{red}{9 x}$

therefore the two right hand sides are also equal

Equate them: " "color(blue)(6y+3) = color(red)(4y+17

$\textcolor{w h i t e}{w w w w w w w w w .} 6 y - 4 y = 17 - 3$

$\textcolor{w h i t e}{w w w w w w w . w w w w .} 2 y = 14$

$\textcolor{w h i t e}{w \ldots \ldots . w w w . w w w w w .} y = 7$

Substitute $7$ for $y$ to find the value of $x$

$\textcolor{w h i t e}{w w w w w w w w w .} 9 x = 6 \left(7\right) + 3$

$\textcolor{w h i t e}{w w w w w w w w w .} 9 x = 45$

$\textcolor{w h i t e}{w w w w w w w . w w .} x = 5$