how do you do equations where they don't give you y to start like

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

-4x +y =6

y = 6 + 4x

Then use (6+4x) for y in the second equation.

To solve a system of equations, you can use either the substitution or the elimination method. In this case, let's use the elimination method:

Step 1: Multiply the first equation by -1 to change the signs of all terms.
-4x + y = 6 (equation 1)
-(-5x -y) = -21 (equation 2)

This gives us:
4x - y = -6 (equation 3)
5x + y = 21 (equation 4)

Step 2: Add equation 3 and equation 4 together to eliminate the variable y.
(4x - y) + (5x + y) = -6 + 21
4x - y + 5x + y = 15x = 15

Simplifying:
9x = 15

Step 3: Solve for x by dividing both sides of the equation by 9.
9x/9 = 15/9
x = 5/3

Step 4: Substitute the value of x back into one of the original equations to solve for y. Let's use equation 1.
-4(5/3) + y = 6

Simplifying:
-20/3 + y = 6
y = 6 + 20/3
y = (18 + 20)/3
y = 38/3

Therefore, the solution to the system of equations is x = 5/3 and y = 38/3.