4.1: Substitution and Elimination | Algebra 1 Honors

How it works

A solution of a system satisfies every equation simultaneously. Substitution replaces one variable using an equivalent expression. Elimination combines equations to remove a variable. Choose the method that keeps arithmetic clear, then check the ordered pair in both original equations.

\text{A system solution lies on every equation in the system.}

Worked examples

Example 1

Solve $\displaystyle y=x+1$ and $\displaystyle 2x+y=7$ .

Substitute: $\displaystyle 2x+x+1=7$ , so $\displaystyle x=2$ and $\displaystyle y=3$ . Both original equations hold.

Example 2

Solve $\displaystyle x+y=9$ and $\displaystyle x-y=3$ .

Add the equations: $\displaystyle 2x=12$ , so $\displaystyle x=6$ . Substitute to obtain $\displaystyle y=3$ .

Problems

Problem 4.1.1

Solve $\displaystyle y=2x$ and $\displaystyle x+y=12$ .

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$\displaystyle x+2x=12$ , so $\displaystyle x=4$ and $\displaystyle y=8$ .

Problem 4.1.2

Solve $\displaystyle 2x+y=8$ and $\displaystyle 2x-y=4$ .

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Add: $\displaystyle 4x=12$ , giving $\displaystyle x=3$ . Then $\displaystyle y=2$ .

Problem 4.1.3

Use the graph to solve the system $\displaystyle y=x+1$ , $\displaystyle y=-x+5$ .

The lines y = x + 1 and y = −x + 5 cross once. — The solution must lie on both lines.

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The two lines meet at $\displaystyle (2,3)$ . Algebra confirms $\displaystyle x+1=-x+5$ , so $\displaystyle x=2$ and $\displaystyle y=3$ .

The lines y = x + 1 and y = −x + 5 cross once. The intersection is (2, 3). — The intersection is (2, 3).

Lesson Problems PDF Solutions PDF Unit MCQ

How it works

Worked examples

Example 1

Example 2

Problems

Problem 4.1.1

Problem 4.1.2

Problem 4.1.3

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