Chapter 2: Q8. (page 69)

Solve each system of equations by the substitution method.
$x - 7 y = 13$
$3 x - 5 y = 23$

Short Answer

Expert verified

The solution of given system of equations is x = 6, y = – 1.

Step by step solution

Step 1. Substitute value of one variable from one equation to another.

Add 7y on both the sides of $x - 7 y = 13$ and simplify.

$x - 7 y + 7 y = 13 + 7 y$

$x = 13 + 7 y$

Substitute $13 + 7 y$ for into $3 x - 5 y = 23$ and simplify.

$3 (13 + 7 y) - 5 y = 23$

$39 + 21 y - 5 y = 23$

$39 + 16 y = 23$

$16 y = - 16$

Step 2. Solve for one variable.

Divide each side of the equation obtained in step 2 by 16 to find the value of y.

$\frac{16 y}{16} = \frac{- 16}{16}$

$y = - 1$

Step 3. Solve for another variable.

Substitute $- 1$ for into $x - 7 y = 13$ , to find the value of x.

$x - 7 (- 1) = 13$

$x + 7 = 13$

$x = 6$

Therefore, the solution of given system of equations isx = 6, y = – 1.

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Solve each system of equations by the substitution method.
$x - 7 y = 13$
$3 x - 5 y = 23$

Short Answer

Step by step solution

Step 1. Substitute value of one variable from one equation to another.

Step 2. Solve for one variable.

Step 3. Solve for another variable.

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Solve each system of equations by the substitution method.x–7y=133x–5y=23

Short Answer

Step by step solution

Step 1. Substitute value of one variable from one equation to another.

Step 2. Solve for one variable.

Step 3. Solve for another variable.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Theoretical and Mathematical Physics

Calculus

Geometry

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Solve each system of equations by the substitution method.
$x - 7 y = 13$
$3 x - 5 y = 23$