Solve the following system of linear equations: 2x + y = 4, 3x + 4y = 7

May 15, 2026Mathematics

ScanSolve AI Answer

May 15, 2026

Answer

$x=\frac{9}{5}, y=\frac{2}{5}$

Given the system of equations: $\begin{cases} 2x + y = 4 \quad &(1) \\ 3x + 4y = 7 \quad &(2) \end{cases}$

Step 1: Multiply equation (1) by 4 to make the coefficients of $y$ equal. $4(2x + y) = 4(4)$ $8x + 4y = 16 \quad &(3)$

Step 2: Subtract equation (2) from equation (3) to eliminate $y$ . $(8x + 4y) - (3x + 4y) = 16 - 7$ $8x + 4y - 3x - 4y = 9$ $5x = 9$

Step 3: Solve for $x$ . $x = \frac{9}{5}$

Step 4: Substitute the value of $x$ into equation (1) to find $y$ . $2\left(\frac{9}{5}\right) + y = 4$ $\frac{18}{5} + y = 4$ $y = 4 - \frac{18}{5}$ $y = \frac{20}{5} - \frac{18}{5}$ $y = \frac{2}{5}$ The solution is $\boxed{x=\frac{9}{5}, y=\frac{2}{5}}$ .

That's 2 down. 3 left today — send the next one.

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

Qनिम्नलिखित प्रश्नों के उत्तर दीजिए: A. रिक्त स्थानों की पूर्ति कीजिए - B. Fill in the blanks - C. सत…QGuys what is the standard hight of a water closet if the diameter is 100mm Q8 . Calculate the area of triangle given below with scale 1cm to 4km . 9 What point of the compass c…QDetermine the equation that Mr. Kheswa will use to calculate his total monthly costs.QUse the information and Table 1 above to answer the questions that follow. 15.1.1 Differentiate betw…

See all Mathematics questions →

Still have questions?

Quick Answer

Given the system of equations: 2x + y = 4 &(1) \\ 3x + 4y = 7 &(2) Step 1: Multiply equation (1) by 4 to make the coefficients of y equal.

Asked on May 15, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 15, 2026

Given the system of equations: 2x + y = 4 &(1) \\ 3x + 4y = 7 &(2) Step 1: Multiply equation (1) by 4 to make the coefficients of y equal. 4(2x + y) = 4(4) 8x + 4y = 16 &(3) Step 2: Subtract equation (2) from equation (3) to eliminate y. (8x + 4y) - (3x + 4y) = 16 - 7 8x + 4y - 3x - 4y = 9 5x = 9 Step 3: Solve for x. x = (9)/(5) Step 4: Substitute the value of x into equation (1) to find y. 2((9)/(5)) + y = 4 (18)/(5) + y = 4 y = 4 - (18)/(5) y = (20)/(5) - (18)/(5) y = (2)/(5) The solution is x=(9)/(5), y=(2)/(5). That's 2 down. 3 left today — send the next one.

Asked on May 15, 2026Mathematics

ScanSolve AI AnswerAnswered on May 15, 2026

Given the system of equations: 2x + y = 4 &(1) \\ 3x + 4y = 7 &(2) Step 1: Multiply equation (1) by 4 to make the coefficients of y equal. 4(2x + y) = 4(4) 8x + 4y = 16 &(3) Step 2: Subtract equation (2) from equation (3) to eliminate y. (8x + 4y) - (3x + 4y) = 16 - 7 8x + 4y - 3x - 4y = 9 5x = 9 Step 3: Solve for x. x = (9)/(5) Step 4: Substitute the value of x into equation (1) to find y. 2((9)/(5)) + y = 4 (18)/(5) + y = 4 y = 4 - (18)/(5) y = (20)/(5) - (18)/(5) y = (2)/(5) The solution is x=(9)/(5), y=(2)/(5). That's 2 down. 3 left today — send the next one.