Solve the system of equations.%0D%0A3x+6y=21%0D%0A3%0D%0A%0D%0A+%0D%0A6%0D%0A%0D%0A=%0D%0A21%0D%0A%0D%0A–5x+2y=13%0D%0A–%0D%0A5%0D%0A%0D%0A+%0D%0A2%0D%0A%0D%0A=%0D%0A13%0D%0A(1 point)%0D%0A(, )

Answer 1

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

From the first equation: 3x + 6y = 21, we can rewrite it as x = (21 - 6y) / 3.

Substituting this value into the second equation, -5x + 2y = 13, we have:
-5((21 - 6y) / 3) + 2y = 13
Multiplying both sides of the equation by 3 to eliminate the fraction:
-5(21 - 6y) + 6y = 39
Multiply through:
-105 + 30y + 6y = 39
Combine like terms:
36y = 144
Divide both sides of the equation by 36 to solve for y:
y = 4

Next, we substitute this value of y back into the first equation to solve for x:
3x + 6(4) = 21
3x + 24 = 21
Subtract 24 from both sides of the equation:
3x = -3
Divide both sides of the equation by 3 to solve for x:
x = -1

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