Answer: (1, -4), or x = 1 and y = -4
Step-by-step explanation:
We can solve this system of equations in multiple different ways, I will show two methods. The first method is to solve by graphing, see attached. The point of intersection is our solution. This tell us that the answer is (1, -4), or x = 1 and y = -4.
The second method is to solve with substitution. We will substitute the first equation, solved for x, into the second and solve for y. Then, substitute this value of y into one of the equations to solve for x.
x - 5y = 21 ➜ x = 5y + 21
Given:
3x - 4y = 19
Substitute:
3(5y + 21) - 4y = 19
Distribute:
15y + 63 - 4y = 19
Combine like terms:
11y + 63 = 19
Subtract 63 from both sides of the equation:
11y = -44
Divide both sides of the equation by 11:
y = -4
Solve for x:
x = 5y + 21
Substitute:
x = 5(-4) + 21
Compute:
x = 1
