Question:
i.Complete the following activity and find the value of \(x\):
\[
\begin{aligned}
5x + 3y &= 9 \quad \text{...(I)} \\
2x - 3y &= 12 \quad \text{...(II)}
\end{aligned}
\]
i.Complete the following activity and find the value of \(x\):
\[ \begin{aligned} 5x + 3y &= 9 \quad \text{...(I)} \\ 2x - 3y &= 12 \quad \text{...(II)} \end{aligned} \]
\[ \begin{aligned} 5x + 3y &= 9 \quad \text{...(I)} \\ 2x - 3y &= 12 \quad \text{...(II)} \end{aligned} \]
Show Hint
When two linear equations have opposite coefficients for one variable, adding or subtracting them eliminates that variable — making it easier to solve for the other one.
Updated On: Nov 6, 2025
Show Solution
Verified By Collegedunia
Solution and Explanation
Step 1: Write down the two equations.
\[ \text{(I)} \; 5x + 3y = 9 \] \[ \text{(II)} \; 2x - 3y = 12 \] Step 2: Add equations (I) and (II).
\[ (5x + 3y) + (2x - 3y) = 9 + 12 \] Step 3: Simplify.
\[ 7x = 21 \] Step 4: Solve for \(x\).
\[ x = \frac{21}{7} = 3 \] Step 5: Conclusion.
Hence, the value of \(x\) is 3.
Final Answer: \[ \boxed{x = 3} \]
\[ \text{(I)} \; 5x + 3y = 9 \] \[ \text{(II)} \; 2x - 3y = 12 \] Step 2: Add equations (I) and (II).
\[ (5x + 3y) + (2x - 3y) = 9 + 12 \] Step 3: Simplify.
\[ 7x = 21 \] Step 4: Solve for \(x\).
\[ x = \frac{21}{7} = 3 \] Step 5: Conclusion.
Hence, the value of \(x\) is 3.
Final Answer: \[ \boxed{x = 3} \]
Was this answer helpful?
0
0
Top Maharashtra Class X Board Mathematics Questions
- Out of the following which is a Pythagorean triplet ?
- \(\angle\)ACB is inscribed angle in a circle with centre O. If \(\angle\)ACB = 65\(^{\circ}\), then what is measure of its intercepted arc AXB ?
- Distance of point (3, 4) from the origin is .................. .
- If radius of cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ...................... .
In the following figure \(\triangle\) ABC, B-D-C and BD = 7, BC = 20, then find \(\frac{A(\triangle ABD)}{A(\triangle ABC)}\).
View More Questions
Top Maharashtra Class X Board Algebra Questions
- Complete the following activity to determine the nature of the roots of the quadratic equation \(x^2 + 2x - 9 = 0\):
- Solve the following simultaneous equations: \[ x + y = 4 \quad \text{and} \quad 2x - y = 2 \]
- Write the following equation in the form \(ax^2 + bx + c = 0\), then write the values of \(a, b, c\):
\[ 2y = 10 - y^2 \] - Solve the following simultaneous equations using Cramer’s Rule: \[ 4m + 6n = 54 \quad \text{and} \quad 3m + 2n = 28 \]
- Solve the following quadratic equation by formula method: \[ x^2 + 10x + 2 = 0 \]
View More Questions
Top Maharashtra Class X Board Questions
- Pick out the infinitive from the following sentence :
He was asking to go for the concert. - Identify the type of the sentence:
Get out and wait in the yard. - Arrange the following words in alphabetical order:
inventions, inequality, indisputable, interactions - Complete the word chain of nouns:
Podium, m .........., .........., .........., .......... - Punctuate the following sentence:
can you cook
View More Questions