Solve the following system by the substitution method. Show your work.
{2x−7y=12−x+3.5y=−6
I will assume your equations are:
2x−7y=12 and
−x+3.5y=−6
from the 2nd: x = 3.5y + 6
sub into 1st
2(3.5y+6) - 7y = 12
7y + 12 - 7y = 12
0 = 0, which is a true statement
ahhh, so the two equations actually represent the same line
and of course they would intersect with themselves an infinite
number of times
notice if we multiply the 2nd by -2, we get
2x - 7y = 12, the same as the 1st
i dont get this
Divide 6 by 5 to get your y to sub in for y
Y=-1.2
Substitute 1.2 in for every y you see in the problem
2x-7(-1.2)=12-x+3
2x+8.4=15-x
2x=6.6-x
3x=6.6
Then just divide both sides by 3
X=2.2
So x=2.2 and y=-1.2
Let me know if this helps!😀
Your two equations are:
2x-7y=12
-x+3.5y=-6
First, we have to find the value that is alone in one of the equations and isolate it, which would be -x in the second equation. To isolate the -x, we must move y to the other side.
-x+3.5y=-6
-3.5y -3.5y
Which leaves use with this:
-x=-6-3.5y
And to make x positive, we divide both sides by -1.
x=6+3.5y
Now that one value is isolated, we can use it in the first equation to solve for y. So we switch every x to 6+3.5y, and then solve the equation.
2(6+3.5y)-7y=12
12+7y-7y=12
12=12
Since the two numbers don't include y and they are equal, there are infinite solutions.
To solve the system of equations by the substitution method, we need to find a variable that we can isolate in one of the equations and substitute it into the other equation.
Let's solve for x in the first equation of the system:
2x - 7y = 12
Isolate x:
2x = 12 + 7y
x = (12 + 7y) / 2
Now, substitute this value of x into the second equation of the system:
- x + 3.5y = -6
-((12 + 7y) / 2) + 3.5y = -6
Multiply all terms in the equation by 2 to eliminate the fraction:
- (12 + 7y) + 7(3.5y) = -12
-12 - 7y + 24.5y = -12
Combine like terms:
17.5y - 7y = 0
10.5y = 0
Divide both sides by 10.5:
y = 0
Now that we have the value of y, we can substitute it back into one of the original equations to find the value of x. Let's use the first equation:
2x - 7(0) = 12
2x = 12
x = 12 / 2
x = 6
So the solution to the system of equations is x = 6 and y = 0.