solve by using subsitution:
4x+y=2
3y+2x=-1
To solve this system of equations using substitution, you need to solve one of the equations for one variable and substitute that expression into the other equation.
Let's solve the first equation for y:
4x + y = 2
Rearrange the equation to isolate y:
y = 2 - 4x
Now, substitute this expression for y in the second equation:
3y + 2x = -1
Replace y with 2 - 4x:
3(2 - 4x) + 2x = -1
Distribute the 3:
6 - 12x + 2x = -1
Combine like terms:
-10x + 6 = -1
Move 6 to the right side:
-10x = -1 - 6
-10x = -7
Divide by -10:
x = (-7) / (-10)
x = 7/10
Now that we have the value of x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
4x + y = 2
Replace x with 7/10:
4(7/10) + y = 2
Multiply 4 by 7/10:
(28/10) + y = 2
Reduce 28/10:
(14/5) + y = 2
Subtract (14/5) from both sides:
y = 2 - (14/5)
y = (10/5) - (14/5)
y = -4/5
So the solution to the system of equations is x = 7/10 and y = -4/5.