Solve the system of equations : 2x+3y=10. 4x+7y=21

Write Equations: Write down the system of equations. We have the following system of linear equations: 2x + 3y = 10 4x + 7y = 21Multiply First Equation: Multiply the first equation by 2 to prepare for elimination. Multiplying the first equation by 2 gives us: 4x + 6y = 20 Now we have: 4x + 6y = 20 4x + 7y = 21Subtract Equations: Subtract the second equation from the first to eliminate x. (4x + 6y) - (4x + 7y) = 20 - 21 This simplifies to: 4x + 6y - 4x - 7y = -1 Which further simplifies to: -y = -1Solve for y: Solve for y. Divide both sides by -1 to get: y = 1Substitute and Solve: Substitute y = 1 into the first original equation to solve for x. Using the first equation 2x + 3y = 10, we substitute y with 1: 2x + 3(1) = 10 2x + 3 = 10Final Solution: Solve for x. Subtract 3 from both sides to isolate 2x: 2x = 10 - 3 2x = 7 Divide both sides by 2 to get: x = 7/2 x = 3.5

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Solve the system of equations : $\newline$ $2x+3y=10$ . $\newline$ $4x+7y=21$

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Grade 7

Solve equations involving like terms

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Q. Solve the system of equations :

\newline

2x+3y=10

\newline

4x+7y=21

Write Equations: Write down the system of equations. $\newline$ We have the following system of linear equations: $\newline$ $2x + 3y = 10$ $\newline$ $4x + 7y = 21$
Multiply First Equation: Multiply the first equation by $2$ to prepare for elimination. $\newline$ Multiplying the first equation by $2$ gives us: $\newline$ $4x + 6y = 20$ $\newline$ Now we have: $\newline$ $4x + 6y = 20$ $\newline$ $4x + 7y = 21$
Subtract Equations: Subtract the second equation from the first to eliminate $x$ . $\newline$ $(4x + 6y) - (4x + 7y) = 20 - 21$ $\newline$ This simplifies to: $\newline$ $4x + 6y - 4x - 7y = -1$ $\newline$ Which further simplifies to: $\newline$ $-y = -1$
Solve for y: Solve for y. $\newline$ Divide both sides by $-1$ to get: $\newline$ $y = 1$
Substitute and Solve: Substitute $y = 1$ into the first original equation to solve for $x$ . Using the first equation $2x + 3y = 10$ , we substitute $y$ with $1$ : $2x + 3(1) = 10$ $2x + 3 = 10$
Final Solution: Solve for $x$ . $\newline$ Subtract $3$ from both sides to isolate $2x$ : $\newline$ $2x = 10 - 3$ $\newline$ $2x = 7$ $\newline$ Divide both sides by $2$ to get: $\newline$ $x = \frac{7}{2}$ $\newline$ $x = 3.5$