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Example1

Title: Linear Equations with Two Variables

Grade Lesson s5-l2

Explanation: The best way to understand SAT-4 is by looking at some examples. Take turns and read each example for easy understanding.

Examples

Topics → Definition Example1

Solve the following system of equations:

2x + 6y = 7
9x - 5y = 11

Step: 1

To solve the system of equations:

2x + 6y = 7 ---(1) 9x - 5y = 11 ---(2)

Explanation:

The provided system of equations is denoted as (1) and (2).

Step: 2

Now use the elimination method:

Multiply equation (1) by 9 and equation (2) by 2 to eliminate the x coefficients:

9(2x + 6y) = 9(7) ⇒ 18x + 54y = 63 ---(3)
2(9x - 5y) = 2(11) ⇒ 18x - 10y = 22 ---(4)

Subtract equation (4) from equation (3) to eliminate the x term:

(18x + 54y) - (18x - 10y) = 63 - 22
18x + 54y - 18x + 10y = 63 - 22
64y = 41

Slove for y value: y = \$ (41)/(64) \$.

Explanation:

Use the elimination method to determine the value of y in the equation and eliminate the x value in the equation.

Step: 3

Substitute the value of y back into equation (1) or (2) to solve for x:

\$ 2x + 6((41)/(64)) = 7\$ (using equation 1)

\$ 2x + (246)/(64) = 7 \$

\$ 2x = 7 - (246)/(64) \$

\$ 2x = (448)/(64) - (246)/(64) \$

\$ 2x = (202)/(64) \$

Slove for x value: \$ x = (101)/(64) \$.

Thus, the solution to the system of equations is \$ x = (101)/(64) \$ and \$y = (41)/(64) \$.

Explanation:

Replace y with a value in equation (1) or (2) to find x, then simplify for the x value in the equation.