Question

Solve the system of equations.
3x+6y=21
–5x+2y=13 (1 point)

Answer 1

To solve the system of equations, we can use the method of substitution.

First, let's solve one of the equations for one variable in terms of the other variable.

We can rearrange the first equation, 3x + 6y = 21, to get:
3x = 21 - 6y
Dividing both sides by 3, we get:
x = 7 - 2y (Equation 1)

Now, we can substitute this expression for x into the second equation.

Substituting x = 7 - 2y into the second equation -5x + 2y = 13, we have:
-5(7 - 2y) + 2y = 13
Distributing the -5, we get:
-35 + 10y + 2y = 13
Combining like terms, we have:
12y - 35 = 13
Adding 35 to both sides, we get:
12y = 48
Dividing both sides by 12, we find:
y = 4

Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x.

Using Equation 1, x = 7 - 2y, we have:
x = 7 - 2(4)
x = 7 - 8
x = -1

Therefore, the solution to the system of equations is x = -1 and y = 4.