Finding the Y-Value in a System of Linear Equations

Question

Solve the following system of equations for the y-value: x + 2y = 7 and 2x +2y =13

A ) y = 1/2 

B) y=6

C) y=5

D) y=13/4

Answer 1

When I do these type of problems, my strategy or what I wanna think about is

Number one. Recognize that you have two equations with two unknowns. In this case, x and y

Number two. Either add the two equations together or subtract one equation from the other to get a result of having just X or Y remaining.

Number three. To do either the subtraction method or the addition method mentioned above, you may have to multiply through or divide through on one of the equations to get to an equivalent equation that is easy to subtract or add from the other equation to eliminate one of the variables.

In this case, both equations have a 2Y so we can just do equation one minus equation 2 and eliminate the Y variable.

X plus 2Y equals 7

Minus. 2X plus 2Y equals 13.

Equals. Negative X plus 0Y equals -6.

Solving for X you get X equals 6

Number four. After solving for one of the variables, we can then substitute the variable we just solve for and substitute back into one of the original equations and solve for the other variable.

So substituting X equals 6 into the first equation and solving for Y

6+ 2Y equals 7

Subtracting six from both sides 2Y equals 1 remains

Then solving for y by dividing by two on each side, we get Y equals 1/2

In summary. Two unknown variables. Add or subtract the two equations to get one unknown remaining. Solve for a solution. For the other unknown.

as an alternative to above, we could have multiplied the first equation by -2, and then added that equation to the second equation to eliminate X and just have y variable remaining and then solve for y and been done

-2x - 4y = -14

plus. 2x + 2y = 13

Equals. 0 -2y = -1

solving for y. Y = 1/2

Answer 2

Answer 3

Hi Asked

Since the question is to Find the Y-value, I’d recommend just solving for y whether it is done through Elimination, Substitution or Graphing. I will do it with Substitution.

Given

x + 2y = 7

We can easily set up everything in terms of y by using the equation above

x = 7 - 2y

Next just substitute this in the second equation given

2x + 2y = 13

2(7 - 2y) + 2y = 13

14 - 4y + 2y = 13

Combine like terms

-2y = -1

Solve for y

y = 1/2

You can check your value in equation 2, again carrying out the substitution obtained from the first equation.

2(7 - 2(1/2)) + 2(1/2) = 13

2(7 - 1) + 1 = 13

2(6) + 1 = 13

12 + 1 = 13

You can always graph your equations to confirm the value of Y. If you have a graphing calculator or access to desmos.com you can graph your equations on the same grid.

I hope this helps.