I still don't know how to completely solve systems by substitution. Can someone please help me?
1. Y=-11+x
3x+10y=-6
How would you know where to plug in the right section of the equation in a certain place?
2. Y =6x-5
Y =-x+9
substitute the value of a variable from one equation into the other equation. For #1, we are told
y = x-11
So, substitute that into the other equation, and we have
3x + 10(x-11) = -6
3x + 10x - 110 = -6
13x = 104
x = 8
So, y = x-11 = 3
Be sure to check the solution to make sure it satisfies both original equations.
Now do #2 in just the same way.
Okay! On #2 how would you set it up since there's no equal signs
To solve systems of equations by substitution, you need to follow these steps:
1. Choose one equation and solve it for one variable in terms of the other.
For the first system of equations:
Y = -11 + x ----> equation 1
2. Substitute the expression you found for that variable into the other equation.
Substituting equation 1 into the second equation, we get:
3x + 10y = -6
3x + 10(-11 + x) = -6
3. Simplify and solve for the remaining variable.
Expanding and combining like terms, we have:
3x - 110 + 10x = -6
13x - 110 = -6
13x = 104
x = 8
4. Substitute the value you found for that variable back into one of the original equations to solve for the other variable.
Using equation 1:
Y = -11 + x
Y = -11 + 8
Y = -3
So, the solution to the first system of equations is x = 8 and y = -3.
For the second system of equations:
1. Choose one equation and solve it for one variable in terms of the other.
For the second system, we already have both equations in terms of y:
Y = 6x - 5 ----> equation 1
Y = -x + 9 ----> equation 2
2. Set the expressions equal to each other.
6x - 5 = -x + 9
3. Simplify and solve for the remaining variable.
Adding x to both sides:
6x + x - 5 = 9
7x - 5 = 9
7x = 14
x = 2
4. Substitute the value you found for that variable back into one of the original equations to solve for the other variable.
Using equation 1:
Y = 6x - 5
Y = 6(2) - 5
Y = 7
So, the solution to the second system of equations is x = 2 and y = 7.