1. Y=4x+24 and y=^x+6
What the x value is a solution to equation
2 . 4x+5y=7
y=3x+9
^ Solve the system using Substitution show all work
9x+5y=35
2x+5y=0
^ Solve the system using linear Combination Show all work
#1. try substitution. Since y=x+6,
x+6 = 4x+24
x = -6
and y = x+6 = 0
#2. substitution will work here too, since y=3x+9
4x+5(3x+9) = 7
x = -2
and y = 3
#3. use elimination. If you subtract the bottom equation from the top one, you get
7x = 35
x = 5
and y = -2
If these still bother you, you need to review the topic some more, either in your text, or online, where youi will find many examples and videos.
x =
Thank you
1. To find the x value that is a solution to the given equations, we need to set them equal to each other and solve for x. The equations are:
Y = 4x + 24
y = ^x + 6
Since both equations represent the same variable (y), we can set them equal to each other:
4x + 24 = ^x + 6
Now, we can solve for x. Subtract ^x from both sides:
4x - ^x + 24 = 6
Combine like terms:
3x + 24 = 6
Subtract 24 from both sides:
3x = 6 - 24
3x = -18
Finally, divide both sides by 3:
x = -18 / 3
x = -6
Therefore, the x value that is a solution to the given equations is -6.
2. To solve the system of equations using the method of substitution, we will substitute one equation into the other and solve for one variable. The given equations are:
4x + 5y = 7
y = 3x + 9
Let's solve the second equation for y:
y = 3x + 9
Now, we substitute this value of y into the first equation:
4x + 5(3x + 9) = 7
Distribute the 5:
4x + 15x + 45 = 7
Combine like terms:
19x + 45 = 7
Subtract 45 from both sides:
19x = 7 - 45
19x = -38
Finally, divide both sides by 19:
x = -38 / 19
x = -2
Now, substitute this value of x back into the second equation to find y:
y = 3(-2) + 9
y = -6 + 9
y = 3
Therefore, the solution to the system of equations is x = -2 and y = 3.
3. To solve the system of equations using the method of linear combination (also known as elimination), we will add or subtract the equations in a way that eliminates one variable. The given equations are:
9x + 5y = 35
2x + 5y = 0
To eliminate the variable y, we will multiply the second equation by -1:
-1(2x + 5y) = -1(0)
-2x - 5y = 0
Now, we can add the two equations:
9x + 5y + (-2x - 5y) = 35 + 0
9x - 2x + 5y - 5y = 35
7x = 35
Divide both sides by 7:
x = 35 / 7
x = 5
Now, substitute this value of x back into either equation (let's use the second equation) to find y:
2(5) + 5y = 0
10 + 5y = 0
5y = -10
Divide both sides by 5:
y = -10 / 5
y = -2
Therefore, the solution to the system of equations is x = 5 and y = -2.