Solve by substitute:
1) y=2x-1
2x+2y=22
Solove by emlimination:
1) 5x+4y=-83
3x-3y=-12
Solve using a method of your choice:
1) x+2y=23
5x+10y=55
2) y=x+1
2x-2y=-2
Please help me I don't understand any of this, it's my second day of school and I already feel like a failure and im on the verge of crying
when it says substitution, use the value from one equation to solve the other.
y = 2x-1, so the 2nd equation becomes
2x+2(2x-1) = 22
2x + 4x - 2 = 22
6x = 24
x = 4
Using elimination, find ways to make one variable disappear by adding the two equations (or multiples of them)
5x+4y=-83
3x-3y=-12
to get rid of y, multiply the two equations by 3 and 4, and you have
15x+12y = -249
12x-12y = -48
Now add them up, and y is eliminated:
27x = -297
x = -11
Now use that value in either of the original equations to get y:
3x-3y = -12
3(-11)-3y = -12
-33 - 3y = -12
-3y = 21
y = -7
Surely your text has examples of this. If not, google will produce lots of examples and explanations online.
working with formulas
-x+y=-13 and 3x-y=19
-x+y=-13 and 3x-y=19 solve by substitute
Sol
ve by substitude
I'm sorry to hear that you're feeling overwhelmed. Math can be tough, especially when you're just starting to learn new concepts. But don't worry, we'll take it one step at a time and I'll explain how to solve each problem.
Let's start with the first set of equations and solve them using the method of substitution:
1) y = 2x - 1
2x + 2y = 22
To use substitution, we need to solve one equation for one variable and substitute that expression into the other equation. Let's solve the first equation for y:
y = 2x - 1
Now, substitute this expression for y in the second equation:
2x + 2(2x - 1) = 22
Simplify the equation:
2x + 4x - 2 = 22
6x - 2 = 22
Now, isolate x by adding 2 to both sides of the equation:
6x = 22 + 2
6x = 24
Divide both sides of the equation by 6 to solve for x:
x = 24/6
x = 4
Now that we have the value of x, we can substitute it back into the first equation to find the value of y:
y = 2(4) - 1
y = 8 - 1
y = 7
Therefore, the solution to this system of equations is x = 4 and y = 7.
Now let's move on to the second set of equations and solve them using the method of elimination:
1) 5x + 4y = -83
3x - 3y = -12
To eliminate a variable, we need to multiply one or both equations by appropriate constants so that the coefficients of one variable in both equations will cancel each other out. In this case, let's eliminate the y variable. Multiply the second equation by 4:
4(3x - 3y) = 4(-12)
12x - 12y = -48
Now we can add the two equations together:
(5x + 4y) + (12x - 12y) = -83 + (-48)
17x - 8y = -131
Now we have a new equation with only x and y. Let's solve this equation:
17x - 8y = -131
To isolate either x or y, let's solve for x:
17x = 8y - 131
x = (8y - 131)/17
Since we have an expression for x, we can substitute it back into one of the original equations to find the value of y. Let's use the first equation:
5x + 4y = -83
Substitute the expression for x:
5((8y - 131)/17) + 4y = -83
Now, simplify the equation:
(40y - 655)/17 + 4y = -83
Get rid of the fractions by multiplying everything by 17:
40y - 655 + 68y = -1411
Combine like terms:
108y - 655 = -1411
Now, isolate y by adding 655 to both sides:
108y = -1411 + 655
108y = -756
Divide both sides by 108 to solve for y:
y = -756/108
y = -7
Now that we have the value of y, substitute it back into the expression for x:
x = (8(-7) - 131)/17
x = (-56 - 131)/17
x = -187/17
Therefore, the solution to this system of equations is x = -187/17 and y = -7.
Finally, let's solve the last set of equations using a method of my choice:
1) x + 2y = 23
5x + 10y = 55
In this case, we can solve these equations by using the method of elimination. Notice that if we multiply the first equation by 5, we get the second equation. This means the two equations are proportional and represent the same line. Therefore, every point on the line will satisfy both equations. Hence, there are infinitely many solutions to this system.
To summarize:
1) The first set of equations, solved by substitution, has a solution of x = 4 and y = 7.
2) The second set of equations, solved by elimination, has a solution of x = -187/17 and y = -7.
3) The third set of equations, using my choice of method, has infinitely many solutions.
Remember, it's okay to feel overwhelmed sometimes. Math takes practice, and it's normal to have days when things feel challenging. Don't be too hard on yourself. Take it one step at a time, and if you need additional help, don't hesitate to reach out to your teacher or classmates for support. You've got this!