How do you solve the system #2x-9y=6# and #4x-3y=-7#?

Question

How do you solve the system  #2x-9y=6# and #4x-3y=-7#?

Eva Abramson · Accepted Answer

The solution for the system of equations is:
#color(blue)(x=-27/10, y=-19/15# #2x−9y=6#, multiplying this equation by #2# #color(blue)(4x)−18y=12#........equation #(1)# # color(blue)(4x)−3y=−7#........equation #(2)# Solving through elimination: Subtracting equation #(1)# from #(2)#: # color(blue)(cancel(4x)−3y=−7# #color(blue)(cancel(-4x)+18y=-12# #15y=-19# #color(blue)(y=-19/15# Finding #x# from the first equation : #2x−9y=6# #2x=6+9y# #x=(6+9y)/2# #x=(6+9*(-19/5))/2# #color(blue)(x=-27/10#

Abigail Allen · Answer

undefined To solve the system of equations $2x - 9y = 6$ and $4x - 3y = -7$, you can use the method of substitution or elimination. Let's use the substitution method.

From the first equation, solve for $x$:
$$2x = 9y + 6$$
$$x = \frac{9y + 6}{2}$$

Now substitute this expression for $x$ into the second equation:
$$4\left(\frac{9y + 6}{2}\right) - 3y = -7$$

Simplify and solve for $y$:
$$18y + 24 - 3y = -7$$
$$15y = -31$$
$$y = -\frac{31}{15}$$

Now substitute the value of $y$ back into either of the original equations to find $x$. Let's use the first equation:
$$2x - 9(-\frac{31}{15}) = 6$$

Solve for $x$:
$$2x + \frac{279}{15} = 6$$
$$2x = 6 - \frac{279}{15}$$
$$2x = \frac{90 - 279}{15}$$
$$2x = -\frac{189}{15}$$
$$x = -\frac{189}{30}$$
$$x = -\frac{63}{10}$$

So, the solution to the system of equations is $x = -\frac{63}{10}$ and $y = -\frac{31}{15}$.