## 17Calculus Precalculus - Use Substitution to Solve Systems of Linear Equations

##### 17Calculus

Solve by Substitution

Another technique to solve systems of equations is substitution. Just like graphing, this technique is limited to two equations with two unknowns since higher order systems become quite complicated very quickly. Also this technique will often produce fractions very quickly, making the algebra more difficult. However, this is a handy technique to learn since you will use it later on with more effect.
Here is a good video showing this technique using an example. He doesn't check his answer in this video, which is not something you want to skip. Also, notice that his answer contains fractions, so graphing would not be the way to solve this problem.

### MathOnPoint - Solving Linear Systems Substitution Method [7min-58secs]

video by MathOnPoint

Okay, this technique is pretty easy to understand, so we are going to let you jump right into the practice problems.

Practice

Unless otherwise instructed, solve these linear systems using substitution.

Basic

$$2x+4y=4$$
$$y=x-2$$

Problem Statement

$$2x+4y=4$$
$$y=x-2$$

Solution

### PatrickJMT - 1710 video solution

video by PatrickJMT

Log in to rate this practice problem and to see it's current rating.

$$x+3y=6$$
$$2x+6y=-12$$

Problem Statement

$$x+3y=6$$
$$2x+6y=-12$$

Solution

### PatrickJMT - 1711 video solution

video by PatrickJMT

Log in to rate this practice problem and to see it's current rating.

$$2x-3y=6$$
$$4x-6y=12$$

Problem Statement

$$2x-3y=6$$
$$4x-6y=12$$

Solution

### PatrickJMT - 1712 video solution

video by PatrickJMT

Log in to rate this practice problem and to see it's current rating.

$$x+2y=9$$
$$3x+5y=20$$

Problem Statement

$$x+2y=9$$
$$3x+5y=20$$

Solution

### Khan Academy - 1713 video solution

Log in to rate this practice problem and to see it's current rating.

$$y=3x$$
$$2x+y=-10$$

Problem Statement

$$y=3x$$
$$2x+y=-10$$

Solution

### MIP4U - 1715 video solution

video by MIP4U

Log in to rate this practice problem and to see it's current rating.

$$x-2y=1$$
$$3x-6y=-18$$

Problem Statement

$$x-2y=1$$
$$3x-6y=-18$$

Solution

### MIP4U - 1716 video solution

video by MIP4U

Log in to rate this practice problem and to see it's current rating.

$$x-2y=7$$
$$2y-3x=-1$$

Problem Statement

$$x-2y=7$$
$$2y-3x=-1$$

Solution

### MIP4U - 1717 video solution

video by MIP4U

Log in to rate this practice problem and to see it's current rating.

$$2x-y=-5$$
$$4x-2y=-10$$

Problem Statement

$$2x-y=-5$$
$$4x-2y=-10$$

Solution

### MIP4U - 1718 video solution

video by MIP4U

Log in to rate this practice problem and to see it's current rating.

$$x+3y=12; 2x+y=6$$

Problem Statement

$$x+3y=12; 2x+y=6$$

Solution

### MathOnPoint - 2129 video solution

video by MathOnPoint

Log in to rate this practice problem and to see it's current rating.

Intermediate

Here is a little more difficult problem that consists of 3 equations and 3 unknowns. Try substitution here as well.

$$7x-4y-2z=7; 8x-2y-8z=1; x+2y-6z=-6$$

Problem Statement

$$7x-4y-2z=7; 8x-2y-8z=1; x+2y-6z=-6$$

Solution

### PatrickJMT - 1714 video solution

video by PatrickJMT

Log in to rate this practice problem and to see it's current rating.

When using the material on this site, check with your instructor to see what they require. Their requirements come first, so make sure your notation and work follow their specifications.

DISCLAIMER - 17Calculus owners and contributors are not responsible for how the material, videos, practice problems, exams, links or anything on this site are used or how they affect the grades or projects of any individual or organization. We have worked, to the best of our ability, to ensure accurate and correct information on each page and solutions to practice problems and exams. However, we do not guarantee 100% accuracy. It is each individual's responsibility to verify correctness and to determine what different instructors and organizations expect. How each person chooses to use the material on this site is up to that person as well as the responsibility for how it impacts grades, projects and understanding of calculus, math or any other subject. In short, use this site wisely by questioning and verifying everything. If you see something that is incorrect, contact us right away so that we can correct it.