Math Problem Statement

Solve the system of linear equations: 1. 6m + 6n = 5 2. 3m - 10n + 4 = 0

Solution

The equations in the image you uploaded are as follows:

  1. 6m+6n=56m + 6n = 5
  2. 3m10n+4=03m - 10n + 4 = 0

We can solve this system of linear equations using either substitution or elimination method. Let's solve this step by step.

Step 1: Solve one equation for one variable

From equation (1):
6m+6n=56m=56nm=56n66m + 6n = 5 \quad \Rightarrow \quad 6m = 5 - 6n \quad \Rightarrow \quad m = \frac{5 - 6n}{6}

Step 2: Substitute this into equation (2)

Substitute m=56n6m = \frac{5 - 6n}{6} into 3m10n+4=03m - 10n + 4 = 0: 3(56n6)10n+4=03\left(\frac{5 - 6n}{6}\right) - 10n + 4 = 0 Simplify this expression and solve for nn.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Substitution Method

Formulas

Substitution Method
Linear Equations

Theorems

Substitution in Linear Equations

Suitable Grade Level

Grades 7-9