How do you solve the system #5x + 3y =3# and #x+ 9y = 2#?

Question

Eva Abramson · Accepted Answer

#5x+ 3y =3#......equation#(1)#
#x+ 9y = 2#
#x=color(blue)( 2-9y# .........equation #(2)# Solving by substitution
substituting equation #(2)# in equation #(1)#  #5x + 3y =3#
#5color(blue)((2-9y)) + 3y =3#
# 10 - 45y+ 3y =3#
#-42y=-7#
#color(blue)(y)=1/6# finding the value of #x# by substituting the value of #y# in equation #(2)#
#x= 2-9y#
#x= 2-9(1/6)#
#color(blue)(x)= (12-9)/6 = 3/6 = 1/2# the solution for the system of equations is
#color(blue)( x = 1/2 , y =1/6#

Kennedy Adams · Answer

undefined To solve the system of equations:

5x + 3y = 3
x + 9y = 2

You can use either substitution or elimination method. Let's use the elimination method.

1. Multiply the second equation by 5 to make the coefficients of x in both equations the same:

5(x + 9y) = 5(2)
5x + 45y = 10

2. Now, subtract the first equation from the modified second equation to eliminate x:

(5x + 45y) - (5x + 3y) = 10 - 3
42y = 7

3. Solve for y:

y = 7/42
y = 1/6

4. Substitute the value of y into one of the original equations. Let's use the first equation:

5x + 3(1/6) = 3
5x + 1/2 = 3

5. Solve for x:

5x = 3 - 1/2
5x = 5/2

6. Divide by 5:

x = (5/2) / 5
x = 1/2

So, the solution to the system of equations is x = 1/2 and y = 1/6.

Genesis Allen · Answer

undefined You can solve the system of equations $5x + 3y = 3$ and $x + 9y = 2$ using either the substitution method or the elimination method. Here's how to solve it using the elimination method:

Step 1: Multiply the second equation by 5 to make the coefficients of $x$ in both equations equal.
$5(x + 9y) = 5(2)$
This simplifies to $5x + 45y = 10$.

Step 2: Subtract the first equation from the modified second equation to eliminate $x$.
$5x + 45y - (5x + 3y) = 10 - 3$
This simplifies to $42y = 7$.

Step 3: Solve for $y$.
$y = \frac{7}{42} = \frac{1}{6}$.

Step 4: Substitute the value of $y$ into either of the original equations to solve for $x$.
Using the first equation:
$5x + 3(\frac{1}{6}) = 3$
This simplifies to $5x + \frac{1}{2} = 3$.

Step 5: Solve for $x$.
$5x = 3 - \frac{1}{2} = \frac{5}{2}$
$x = \frac{1}{2}$.

So, the solution to the system is $x = \frac{1}{2}$ and $y = \frac{1}{6}$.