That's a lot of questions...have you considered getting a math tutor if your teacher isn't clear? They make everything so much easier, so quickly.
1. What is the value of the x variable in the solution to the following system of equations?
3x + 2y = 6
2x + 3y = −1
This problem can be done two ways, but I prefer to use the elimination method. This means you do something to the equations, then add them together, and one of your variables is eliminated. This can be done because as long as you do the same thing to both sides of an equation, it doesn't actually change. For these two, I recommend multiplying your first equation by -2, and your second equation by 3.
-2(3x) + -2(2y) = -2(6) becomes -6x + -4y = -12
3(2x) + 3(3y) = 3(−1) becomes 6x + 9y = -3
now add these equations together. Everything on the left stays left, everything right stays right.
-6x + -4y = -12
6x + 9y = -3
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5y = -15
The x has been eliminated, because they canceled out. Now solve for y.
5y = -15
y = -3
Use this y to solve for x in your original equations.
3x + 2(-3) = 6
3x - 6 = 6
3x = 12
x = 4
2x + 3(-3) = −1
2x - 9 = -1
2x = 8
x = 4
I'll add the others in a moment...
4.Solve the following system. This is just substitution. Use what you know about y from the first equation to get rid of the variable in the second equation.
y = x + 3
2x + y = 9 becomes 2x + x + 3 = 9
2x + x + 3 = 9
3x + 3 = 9
3x = 6
x = 2
Now use x to solve your first equation.
y = x + 3
y = 2 + 3
y = 5
5. For the following system, if you isolated x in the second equation to use the Substitution Method, what expression would you substitute into the first equation? Just isolate y to find out.
3x + y = 8
−x − y = −7 becomes -y = x - 7 then get rid of the - sign, y = -x + 7
you'd substitute -x + 7
6. b. This becomes obvious if you just follow the math. He added 6x + x and came up with 5x.
7. 7. Solve the following system. This is just substitution again.
x − y = 10 becomes x = 10 + y
x + y = 2 becomes 10 + y + y = 2 becomes 10 + 2y = 2
10 + 2y = 2
2y = -8
y = -4
plug this back in to your equations
x - (-4) = 10
x + 4 = 10
x = 6
x + (-4) = 2
x - 4 = 2
x = 6
8.You graph a system of equations and get two lines that are parallel. Explain what this tells you about the:
they both have the same slope