use the substitution method to solve the linear system.
1. 3x=9
-x+2y=9
3x/3 = 9/3
x = 3
-x(3)+2y = 9
-3+2y = 9
2y = 12
y = 6
is (3,6) correct?
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also, can you please tell me how to solve these?
use the linear combinations to solve the linear system:
2.x+y=3
x+2y=6
3. x+y=7
y=-2x+8
thanks
Yes, on (3.6)
2)
x+y=3
x+2y=6
subtract the second equation from the first:
x+y=3
-(x+2y=6)
or the result is -y=-3
y=3
then go back and solve for x.
To solve a linear system using the substitution method, follow these steps:
1. Solve one equation for one variable in terms of the other variable.
2. Substitute the expression found in step 1 into the other equation.
3. Solve the resulting equation for the remaining variable.
4. Substitute the value found in step 3 back into the expression from step 1 to find the value of the other variable.
Let's solve the linear system mentioned:
1. 3x = 9 => divide both sides by 3, we get x = 3.
2. Substitute x = 3 into the second equation: -x + 2y = 9.
-3 + 2y = 9.
Solve this equation for y: 2y = 9 + 3, so 2y = 12.
Divide both sides by 2, we get y = 6.
So the solution to the linear system is x = 3, y = 6. (3, 6) is indeed correct.
For the additional linear systems:
2. Linear combinations method:
- Multiply the first equation by 2 to make the coefficients of y match:
2(x + 2y) = 2(6) => 2x + 4y = 12.
- Subtract the second equation from this new equation:
2x + 4y - (x + 2y) = 12 - 3 => x = 9.
- Substitute x = 9 back into the first equation:
2(9) + y = 3 => 18 + y = 3.
- Solve this equation for y: y = 3 - 18, y = -15.
So the solution is x = 9, y = -15. (9, -15)
3. Linear combinations method:
- Substitute y = -2x + 8 into the first equation:
x + (-2x + 8) = 7.
- Simplify and solve for x: -x + 8 = 7, x = 1.
- Substitute x = 1 back into the second equation:
y = -2(1) + 8, y = 6.
The solution is x = 1, y = 6. (1, 6)
Hope this explanation helps!