solve by using subsitution:
4x+y=2
3y+2x=-1
To solve the system of equations by substitution, we need to isolate one variable in one equation and substitute it into the other equation. Let's start with the first equation and solve for y in terms of x.
1) 4x + y = 2
To isolate y, subtract 4x from both sides:
y = 2 - 4x
Now, substitute this expression for y into the second equation:
2) 3y + 2x = -1
Replace y with 2 - 4x:
3(2 - 4x) + 2x = -1
Distribute 3 to the terms inside the parentheses:
6 - 12x + 2x = -1
Combine like terms:
-10x + 6 = -1
Now, we need to solve for x. Subtract 6 from both sides:
-10x = -7
To isolate x, divide both sides by -10:
x = (-7) / (-10) = 7/10
We have found the value of x to be 7/10. Now, substitute this value of x back into either of the original equations to solve for y. Let's use the first equation:
4x + y = 2
Replace x with 7/10:
4(7/10) + y = 2
Multiply:
28/10 + y = 2
Simplify:
14/5 + y = 2
Subtract 14/5 from both sides:
y = 2 - 14/5 = 10/5 - 14/5 = -4/5
Therefore, the solution to the system of equations is x = 7/10 and y = -4/5.