solve the system by the method of substitution

x-4y=-21
3x+y=2

I got (0,2)

Try plugging in x=0 and y=2 into your first equiation and uopu will that your answer must be wrong.

Do it this way:

x - 4y =-21
12x+ 4y =8

13 x = -13
x = -1
y = 2 - 3x = ?

x=0 and y=2 does not satisfy the first equation.
(0)-4(2)=0-8=-8 but that isn't equal to -21.

To solve the system by substitution, we'll solve one equation for one variable and substitute it into the other equation. Here's how you can do it step by step:

1. Start with the given system of equations:
x - 4y = -21 ...(Equation 1)
3x + y = 2 ......(Equation 2)

2. Solve Equation 2 for one variable. Let's solve it for y:
3x + y = 2
y = 2 - 3x

3. Substitute the expression for y from Equation 2 into Equation 1:
x - 4(2 - 3x) = -21

4. Simplify the equation:
x - 8 + 12x = -21
13x - 8 = -21

5. Add 8 to both sides of the equation:
13x = -13

6. Divide both sides of the equation by 13:
x = -1

7. Substitute the value of x into Equation 2 to find y:
3(-1) + y = 2
-3 + y = 2
y = 5

Therefore, the solution to the system of equations is x = -1 and y = 5, not (0, 2) as you initially stated.

It's always good to double-check your solution by substituting the values back into the original equations. If they satisfy both equations, then your solution is correct. In this case, (x = -1, y = 5) satisfies both equations, so it is the true solution to the system.