y=3x+11
2x+y=1
method: __________
x= ____________
y= _____________
y=3x+11
2x+y=1
2x + 3x + 11 = 1
5x = -10
x = -2
Now, substitute - 2 for x in the first equation to find the value of y.
thanks.
one more...
x+4y=12
2x-3y=6
How do you know if it's substitution or what?
I used substitution. Why don't you try substitution on the last set of equations?
I'll be glad to check your answer.
To start you off --
x = 12 - 4y
2+12-4y-3y=6
14-7y=6
-7y=-8
y=8/7
x+4(8/7)=12
x+32/7=12
x=52/7
Is that right? My teacher said something to us about that you shouldn't have fractions.
To solve the given system of equations:
1. Choose a method:
- Substitution method: Solve one equation for one variable and substitute it into the other equation.
- Elimination method: Multiply one or both of the equations by suitable constants to eliminate one variable when the equations are added or subtracted.
Let's solve this system using the substitution method:
2. Choose one of the equations to solve for one variable.
Let's solve the first equation, y = 3x + 11, for y.
y = 3x + 11
3. Substitute the value of y derived from step 2 into the other equation.
The other equation is 2x + y = 1.
2x + (3x + 11) = 1
4. Simplify the equation by combining like terms.
2x + 3x + 11 = 1
5x + 11 = 1
5. Solve the resulting equation for x.
Subtract 11 from both sides to isolate x.
5x = 1 - 11
5x = -10
Divide both sides by 5.
x = -10/5
x = -2
6. Substitute the value of x found in step 5 into either equation to solve for y.
Let's substitute x = -2 into y = 3x + 11.
y = 3(-2) + 11
y = -6 + 11
y = 5
Therefore,
- The method used to solve the system of equations is the substitution method.
- The value of x is -2.
- The value of y is 5.