Question

Solve the system of equations by substitution. What is the solution for x? (1 point)
2x + y = 1
4x + 2y = -2


x = 0
x = 2
There is no x value, as there is no solution.
x can be any value as, there is an infinite number of solutions.

HELP PLZ MORE COMING :)
Thank you for your help!

Answer 1

Is this what you mean?

2x + y = 1

y=mx+b

y=-2x+1

; y=(fx)

f(x)=-2x+1

Example: x=5
f(5)=-2(5)+1
f(5)=-10+1
f(5)=-9

;therefore if x=5 then y=9

Answer 2

Substitution means you take one of the equations, solve it for one of the variables in terms of the other(s), then substitute that expression in place of that variable in the other equations. Repeat until you're left with a single equation in a single variable, which you solve to get the value of that variable. Then you work backwards, plugging in the value you found into a previous equation and solving for another variable's value, until you have them all.

Here you have
\[2x + y = 1\]\[4x + 2y = -2\]
Rather than doing your homework for you, I will do a similar problem. Do not use my answer or you will get it wrong. This is an illustration of how to solve by substitution, not a working of your problem.

\[x+y = 4\]\[4x+2y = -2\]

I'll solve the first equation for \(x\) and substitute it in the second.
\[x+y = 4\]\[x + y - y = 4 - y\]\[x = 4-y\]Now everywhere I find \(x\) in the second equation, I replace it with \((4-y)\):
\[4x+2y = -2\]\[4(4-y) + 2y = -2\]\[16 - 4y + 2y = -2\]\[16-2y = -2\]\[16-16-2y = -2-16\]\[-2y = -18\]\[y=9\]

Now I plug \(y=9\) into the substitution equation \(x = 4-y\) to find the value of \(x\):
\[x = 4-y\]\[x = 4-9\]\[x=-5\]

Checking my answer in BOTH equations (necessary because you can get an answer that works for only one if you make a mistake):

\[x+y = 4\]\[-5+9 = 4\]\[4=4\checkmark\]Works in the first equation, let's try the second:\[4x+2y=-2\]\[4(-5)+2(9) = -2\]\[-20+18=-2\]\[-2=-2\checkmark\]Okay, works in both equations, solution is correct.

Note that sometimes you will get a result when solving that gives you something like \[0=0\]This means your equations are equivalent, and there are infinitely many solutions.

Sometimes you get a statement like \[1 = 2\]. This means that there are no solutions to your system. The equations are for parallel lines, which will never intersect to give a solution.