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### Course: Get ready for Algebra 2>Unit 2

Lesson 4: Solving systems of equations with substitution

# Systems of equations with substitution: -3x-4y=-2 & y=2x-5

Learn to solve the system of equations -3x - 4y = -2 and y = 2x - 5 using substitution. Created by Sal Khan.

## Want to join the conversation?

• In a former video, an evil advice-giver dude was humiliated by a smart talking bird. How Sal came up with that, I have no freaking clue.
• Every time there is a video about systems of equations with substitution there is always 2 equations. Could you find the values of x and y (if you had 2 unknown variables) with only one equation?
• If you have one equation with 2 variables (or a linear equation like 2x + 5y = 20), there are an infinite set of solutions. This type of equation creates a line where each point on the line represents an (x, y) ordered pair that is a solution to the equation.

When you have 2 equations with the same 2 variables, then you have a system of linear equations. The solution to the system is the point (or points) that the 2 linear equations have in common.

Hope this helps.
• i get how to solve for y but how do you solve for x
• just plug in the value of y into one of the original equations and solve for x
• I am experiencing brain fog. I have a test tmrw. Any advice??
• It’s okay to study the night before the test, but don’t stay up too late studying. It is best to get a good night’s sleep before the test.
• Math is hard
• fact
• …. um..…. question mark?
• In a former video, a king's advisor was humiliated by a smart talking bird who can do math.
• what is 2x=16-8y but you have to substitute x+4y=25 how would you do this
• To substitute, you have two choices to isolate variables, in both equations, solving for x is the easiest. In the first equation, you could divide by 2 to get x=8-4y. If you have 8-4y+4y=25, you end up with 8=25, so there is no solution (lines parallel).
If you subtract 4y in second equation, you get x=25-4y and substituting in first gives 2(25-4y)=16-8y, distribute to get 50-8y=16-8y, so when you add 8y to both sides, 50=16 which also gives no solution.
This can be seen by getting both in slope intercept form:
y=-1/4 x + 2 and y=-1/4 x + 25/4, both have same slope and different intercepts.
• What would 250m = pc be? (p and c are both variables)
• What are other ways of solving systems of equations?
• When substitution method is taught, you are usually also taught the elimination method and graphing methd.

In later classes in Algebra, you would also learn how to use matrices to solve systems of linear equation.
• what about something like this:

43x+6y=87
20x-2y=74

I need to find what x and what y is. I am stuck. Can anyone explain how to do these problems please?
Thanks
• 43x+6y=87
43x=−6y+87
43x/43 = -6y+87/43
x=-6/43y + 87/43

Subsitute -6/43y + 87/43 for x in 20x-2y=74
20x-2y=74
20(-6/43y+87/43)-2y=74
-206/43 y+1740/43 = 74 ( simplify both sides of the equation)
-206/43 y +1740/43 + -1740/43 =74=-1740/43 (add(-1740)/43 to both sides)
-206/43 y = 1442/43 ( divide both sides)
y=-7
Subsitute
x=-6/43 y+87/43
x=-6/43(-7)+87/43 ( simplify)
x=3
x=3 and y=-7