solve with substitution:
4x+y=2
3y+2x=-1
y = 2-4x
Substituting,
3(2-4x) + 2x = -1
6-12x + 2x = -1
-10x = -1-5
-10x = -6
x = 6/10 or 3/5
error.. that's supposed to be
-10x = -1-6
-10x = -7
x = 7/10
im so sorry..
To solve this system of equations using substitution, we can solve one equation for one variable and substitute that expression into the other equation.
Step 1: Solve the first equation for one variable.
Let's solve the first equation, 4x + y = 2, for y:
y = 2 - 4x
Step 2: Substitute the expression for y into the second equation.
Now we substitute this value of y into the second equation, 3y + 2x = -1:
3(2 - 4x) + 2x = -1
Simplify the equation:
6 - 12x + 2x = -1
Combine like terms:
-10x + 6 = -1
Step 3: Solve for x.
Let's isolate x by moving all the terms to one side:
-10x = -1 - 6
-10x = -7
Divide both sides by -10 to solve for x:
x = -7 / -10
Simplify the fraction:
x = 7/10
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Let's substitute x = 7/10 into the first equation, 4x + y = 2:
4(7/10) + y = 2
Simplify:
28/10 + y = 2
Combine the fractions:
28 + 10y = 20
Step 5: Solve for y.
To isolate y, we subtract 28 from both sides:
10y = 20 - 28
10y = -8
Divide both sides by 10 to solve for y:
y = -8/10
Simplify:
y = -4/5
So the solution to the system of equations is x = 7/10 and y = -4/5.
To solve the given system of equations using the substitution method, follow these steps:
Step 1: Solve one equation 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 value of the variable found in step 1 into the other equation.
Now, substitute the expression for y (2 - 4x) into the second equation, 3y + 2x = -1:
3(2 - 4x) + 2x = -1
Step 3: Simplify and solve for x.
Expand and simplify the equation:
6 - 12x + 2x = -1
-10x + 6 = -1
-10x = -1 - 6
-10x = -7
x = (-7)/(-10)
x = 7/10
Therefore, x = 7/10.
Step 4: Substitute the value of x back into one of the original equations to solve for y.
Substitute x = 7/10 into the first equation, 4x + y = 2:
4(7/10) + y = 2
28/10 + y = 2
28 + 10y = 20
10y = 20 - 28
10y = -8
y = (-8)/(10)
y = -4/5
Therefore, y = -4/5.
So, the solution to the system of equations 4x + y = 2 and 3y + 2x = -1 is x = 7/10 and y = -4/5.