solve by using subsitution:
4x+y=2
3y+2x=-1
To solve this system of equations by substitution, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, 4x + y = 2, for y.
y = 2 - 4x
Step 2: Substitute the expression obtained in Step 1 into the other equation.
Substitute y = 2 - 4x into the second equation, 3y + 2x = -1.
3(2 - 4x) + 2x = -1
Step 3: Simplify and solve the resulting equation for x.
Distribute the 3 to both terms inside the parentheses:
6 - 12x + 2x = -1
Combine like terms:
-10x + 6 = -1
Move the constant term to the other side by subtracting 6 from both sides:
-10x = -1 - 6
-10x = -7
Divide both sides of the equation by -10 to solve for x:
x = -7 / -10
x = 0.7
Step 4: Substitute the value of x into one of the original equations to solve for y.
Using the first equation, 4x + y = 2,
4(0.7) + y = 2
2.8 + y = 2
Subtract 2.8 from both sides:
y = 2 - 2.8
y = -0.8
Therefore, the solution to the system of equations is x = 0.7 and y = -0.8.