Question

What is the solution to the system of equations?

Answer 1

-9x = 27
x = -3

-5(-3) - y = 21
15 - y = 21
y = -6

6 = -4(-3) - 6
6 = 12 - 6

Answer 2

$6 = - 4x + y \\ - 5x - y = 21$

Solve the first equation for y

$y = 4x + 6 \\ - 5x - y = 21$

Substitute the given value of y into the equation -5x-y=21

$- 5x - (4x + 6) = 21$

When there is a - in front of an expression in parentheses, change the sign of each term in the expression

$- 5x - 4x - 6 = 21$

Collect like terms

$- 9x - 6 = 21$

Move the constant to the right-hand side and change its sign

$- 9x = 21 + 6$

Add the numbers

$- 9x = 27$

Divide both sides of equation by -3

$x = - 3$

Substitute the given value of x into the equation y=4x+6

$y = 4 \times ( - 3) + 6$

Multiply the numbers

$y = - 12 + 6$

Calculate the difference

$y = - 6$

The possible solution of the system is the ordered pair (x,y)

$(x,y)=(-3,-6)$