Solve each system by substitution. 0.3 x-0.1 y=5 0.15 x+0.1 y=4

Name: Problem 43, Chapter 5: Beginning and Intermediate Algebra
Uploaded: 2020-06-30T04:36:46-08:00
Duration: 4 min 25 s
Channel: Joshua Fischbach
Description: Solve each system by substitution. 0.3 x-0.1 y=5 0.15 x+0.1 y=4

Solve each system by substitution. 0.3 x-0.1 y=5 ...

Key Concepts

System of Linear Equations

A system of linear equations consists of two or more equations that contain the same set of variables, and the goal is to find values for the variables that satisfy all of the equations simultaneously. These systems are foundational in algebra and are used to model numerous real-world problems where multiple conditions must be met at the same time.

Substitution Method

The substitution method is an approach for solving a system of linear equations in which one equation is manipulated to express one variable in terms of the others, and then this expression is substituted into the other equation(s). This method reduces the system to a single equation with one variable, making it easier to solve and then back-substitute to find the remaining variables.

Transcript

00:01 Following this system, because you're given two equations with decimal coefficients, you're going to want to multiply by the denominator of the smallest place value.

00:09 So this is 10th, tenths, and units.

00:11 So that's going to be 10.

00:12 You're going to multiply this entire thing by 10.

00:14 Between which you're going to move the decimal place, one to the right, and all your terms.

00:18 So you're going to get 3x minus 1y is equal to 50.

00:24 And then on the other one here, you see you've got hundreds, tenths, and units.

00:28 So that's going to be multiplying everything to get rid of all the decimals.

00:33 So that means you're going to move it 2 to the right on all your terms.

00:38 And so what you get here is 15x plus 10y is equal to 400.

00:48 Then you're going to get either the x or y by itself in either equation.

00:52 And you just choose whatever is the easiest for you to work with.

00:54 I think that this first equation here is a negative 1y.

00:57 So that's the easiest one to solve because you have a coefficient of 1 or negative 1.

01:02 So let's do that.

01:03 3x minus y is equal to 50.

01:06 And then you want to get the y by itself.

01:08 So i might add y to both sides and then subtract 50 to both sides.

01:13 And what you get is that 3x minus 50 is equal to y.

01:18 And now we're going to take that value of y.

01:22 And we're going to replace y with it, right? we're going to substitute it in for y in the other equation.

01:27 So now we get our step two move, which is that 15x plus 10 times the quantity of y, which is 3x minus 50, is equal to, oh, sorry, my bad...

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