Question

Solve the system of equations.
3x+6y=21

–5x+2y=13
no faction

Answer 1

To solve the system of equations:

1. \( 3x + 6y = 21 \)
2. \( -5x + 2y = 13 \)

We can use the substitution or elimination method. Here, we'll use the elimination method.

First, let's simplify the first equation:

1. From the first equation:
\[
3x + 6y = 21
\]
Divide everything by 3:
\[
x + 2y = 7 \tag{1}
\]

Now we have a simpler first equation:
1. \( x + 2y = 7 \)

Next, let's express \( x \) in terms of \( y \) from equation (1):
\[
x = 7 - 2y \tag{2}
\]

Now, we can substitute equation (2) into the second equation \( -5x + 2y = 13 \):
\[
-5(7 - 2y) + 2y = 13
\]

Expanding this, we get:
\[
-35 + 10y + 2y = 13
\]
Combining like terms:
\[
12y - 35 = 13
\]

Now, add 35 to both sides:
\[
12y = 48
\]

Dividing both sides by 12:
\[
y = 4
\]

Now that we have the value of \( y \), we can substitute it back into equation (2) to find \( x \):
\[
x = 7 - 2(4)
\]
\[
x = 7 - 8
\]
\[
x = -1
\]

Thus, the solution to the system of equations is:
\[
(x, y) = (-1, 4)
\]