solve by using subsitution:
4x+y=2
3y+2x=-1
To solve the system of equations using substitution, we can follow these steps:
Step 1: Solve one equation for one variable in terms of the other variable.
Step 2: Substitute the expression obtained from step 1 into the other equation.
Step 3: Solve the resulting equation for the remaining variable.
Step 4: Substitute the value of the solved variable back into one of the original equations to find the value of the other variable.
Step 5: Write the values of the variables as an ordered pair, which represents the solution to the system of equations.
Let's solve the given system of equations using these steps:
Step 1: Solve the first equation for y in terms of x:
4x + y = 2
y = 2 - 4x
Step 2: Substitute the expression for y into the second equation:
3y + 2x = -1
3(2 - 4x) + 2x = -1
Step 3: Simplify and solve for x:
6 - 12x + 2x = -1
-10x + 6 = -1
-10x = -7
x = (-7)/(-10) = 7/10 = 0.7
Step 4: Substitute the value of x into one of the original equations:
4x + y = 2
4(0.7) + y = 2
2.8 + y = 2
y = 2 - 2.8 = -0.8
Step 5: Write the solution as an ordered pair (x, y):
Solution: (0.7, -0.8)
Therefore, the system of equations is solved, and the solution is (0.7, -0.8).