solve using substitution
4x + 3y= -3
2x + y = -1
thanxz
When we look at the second equation, we can transfer the term 2x to the other side of the equality. We get that:
2x+y = -1
<=> y = -1-2x
when we replace the y in the first equation by the value we just calculated, we get that:
4x + 3y= -3
<=> 4x + 3(-1-2x)=-3
<=> 4x - 3 -6x = -3
<=> -2x=0
<=> x=0
So, we find that x=0. When we replace this value for x in the equation we earlier found for y, we get that:
y=-1-(2*0)=-1
So, we find that x=0 and y=-1
To solve the given system of equations using the substitution method, we need to isolate one variable in one equation and substitute its value into the other equation.
Let's start by solving the second equation for y:
2x + y = -1
Subtract 2x from both sides:
y = -2x - 1
Now we have an expression for y in terms of x.
Next, we substitute this expression for y into the first equation:
4x + 3y = -3
Substitute y = -2x - 1:
4x + 3(-2x - 1) = -3
Simplify:
4x - 6x - 3 = -3
Combine like terms:
-2x - 3 = -3
Add 3 to both sides:
-2x = 0
Divide by -2:
x = 0
Now that we have the value of x, we can substitute it back into either equation to find the value of y. Let's substitute it into the second equation:
2(0) + y = -1
0 + y = -1
y = -1
So, the solution to the system of equations is x = 0 and y = -1.
To summarize:
x = 0
y = -1