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## Pre-algebra

### Course: Pre-algebra>Unit 13

Lesson 2: Solutions to linear equations

# Worked example: solutions to 2-variable equations

How do you check if an ordered pair is a solution to a given equation? You need to plug in the numbers and see what equality results. Watch this video to see a worked example.

## Want to join the conversation?

• At , would the equation y = -2+ 4/3y be equivalent?
• where did this dude go to school. Mans smart
• Massachusetts Institute of Technology (MIT) and University of New Orleans.
• what if you are not given an ordered pair and you have to figure out this equation
• How are you going to create an equation if you are not given at least one ordered pair? The ordered pair could be implied by giving the x or y intercept, but it is still an ordered pair.
• does this cover absolute vale equalities and inequalities
• I saw nothing here about absolute values which would look like "|x|" or |3|=3 or |-3|=3 OR |-9|=9
The best way to think about absolute values is- "No matter the sign (+ or -) the number remains positive, because the absolute value cannot be negative" Hope that helps. Now inequalities, something simple like....... 1<x<3 where "x" is greater then 1 but less then 3.. The interval notation would be (SET BUILDER NOTATION!)----> {x|x>1, x<3} or (INTERVAL NOTATION(WHICH IS INCLUDING A UNION aka "U"))--> (1,x)U(x,3)...... if the sign was a "greater than or equal to, or less than or equal to" then the interval notation would be [1,x]U[x,3].... I hope this helps.
• What is an "ordered" pair?
• A point on the coordinate plane that gives the horizontal distance from the origin (x) and the vertical distance (y) that is in the form (x,y). If you create a table from a linear equation, you get a series of ordered pairs.
• can't you simplify the equation first? like 4x + 3y = 6?
• You sure can - if you think that will help you.
Look what happened in your case: 4x - 1 = 3y + 5 simplifies to 4x - 3y = 6 not 4x + 3y = 6

Keep Studying!
• how do you figure the value of x and y
• You can pick any number to use for one of the variables. Plug it into the equation to calculate the other variable. For example: 2x+3y=12
If x=2: 2(2)+3y = 12
-- Simplify: 4+3y = 12
-- Subtract 4 from both sides: 3y = 8
-- Divide both sides by 3: y = 8/3 or 2 2/3
-- You now have a point on the line: (2, 2 2/3)

In the video, Sal is given points to test. In that situation, you replace each variable with their given value and see if the 2 sides are equal. Remember, ordered pairs are always (x,y). So, the first value is X and the 2nd value is Y.

Hope this helps.
• between x and y what is the slope and the intercept?
• Most lines have 2 intercepts: an x-intercept and a y-intercept. The x-intercept occurs where y=0 which places the point on the x-axis. The y-intercept occurs where x=0 which places the points on the y-axis.

Lines that have only one intercept are: a) Lines that cross both the x & y axis at the origin (0,0), and b) vertical and horizontal lines which only cross one axis.

To find the slope of a line, you need two points that are on the line, then you would use the slope formula: m = (y2-y1)/(x2-x1). Or, if your equation is in slope intercept form (y = mx + b), then you can read the slope from the line. The number (m) that is the coefficient of "x" is the slope. And, the constant term (b) is the y-intercept at (0,b).
• solve the following systems of linear equations by elimination
12x+5y=23
2x-7y=39
• Add two times the first equation to the second equation to eliminate x:

12x + 5y = 23
2x - 7y = 39

(12x + 5y) + 2(2x - 7y) = 23 + 2 * 39

26x - 18y = 101

So, y = (26x - 101) / -18. Substitute the expression for y back into the first equation to solve for x:

12x + 5y = 23

12x + 5((26x - 101) / -18) = 23

Expand the right side and simplify:

12x + (130x - 505) / -18 = 23

-6x - 505 / -18 = 23

Multiply both sides by -18 to get rid of the fraction:

6x + 505 = -414

Subtract 505 from both sides to isolate x:

6x = -919

Divide both sides by 6 to find x:

x = -153

Finally, substitute the value of x back into the expression for y:

y = (26x - 101) / -18

y = (26 * -153 - 101) / -18

y = 24.

The solution is x = -153 and y = 24.