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Solve Systems of Equations by Substitution: example 5.16 · Physics Playground

Exercises Systems of equations

Example 5.16 from Elementary Algebra, 5.2 Solve Systems of Equations by Substitution

Solve Systems of Equations by Substitution: example 5.16

Solve the system by substitution. ${\begin{matrix} x - 2 y = −2 \\ 3 x + 2 y = 34 \end{matrix}$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution

We will solve the first equation for $x$ and then substitute the expression into the second equation.


Solve for x. Substitute into the other equation.
Replace the x with 2y − 2.
Solve the resulting equation for y.
Substitute y = 5 into x − 2y = −2 to find x.
The ordered pair is (8, 5).
Check the ordered pair in both equations: $\begin{matrix} \begin{matrix} x - 2 y & = & - 2 \\ 8 - 2 \cdot 5 & \overset{?}{=} & - 2 \\ 8 - 10 & \overset{?}{=} & - 2 \\ - 2 & = & - 2 ✓ \end{matrix} & \begin{matrix} 3 x + 2 y & = & 34 \\ 3 \cdot 8 + 2 \cdot 5 & \overset{?}{=} & 34 \\ 24 + 10 & \overset{?}{=} & 34 \\ 34 & = & 34 ✓ \end{matrix} \end{matrix}$
	The solution is (8, 5).

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Solve the system by substitution. ${\begin{matrix} x - 5 y = 13 \\ 4 x - 3 y = 1 \end{matrix}$

How did it go?

PreviousSolve Systems of Equations by Substitution: example 5.15 Next Solve Systems of Equations by Substitution: example 5.17

From Elementary Algebra (1st edition) by OpenStax (Rice University), section 5.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.