Solve for x and y, 2x+3y=5, 3x + 2y = 6.

Write Equations: Write down the system of equations. 2x + 3y = 5 ...(1) 3x + 2y = 6 ...(2)Multiply Equations: Multiply equation (1) by 3 and equation (2) by 2 to make the coefficients of x the same. 3*(2x + 3y) = 3*5 ...(3) 2*(3x + 2y) = 2*6 ...(4)Perform Multiplication: Perform the multiplication. 6x + 9y = 15 ...(5) 6x + 4y = 12 ...(6)Eliminate x: Subtract equation (6) from equation (5) to eliminate x. (6x + 9y) - (6x + 4y) = 15 - 12Simplify Equation: Simplify the equation. 6x - 6x + 9y - 4y = 15 - 12 0x + 5y = 3 5y = 3Solve for y: Solve for y. y = 3/5Substitute y for x: Substitute y = 3/5 into equation (1) to solve for x. 2x + 3*(3/5) = 5Perform Multiplication: Perform the multiplication. 2x + 9/5 = 5Combine Fractions: Convert 5 to a fraction with a denominator of 5 to combine with 9/5. 2x + 9/5 = 25/5Subtract Fractions: Subtract 9/5 from both sides. 2x = 25/5 - 9/5 2x = 16/5Solve for x: Solve for x. x = (16/5) / 2 x = 16/5 * 1/2 x = 16/10 x = 8/5

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Algebra 1

Square roots

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Q. Solve for

x

and

y

\newline

2x+3y=5

\newline

3x + 2y = 6

Write Equations: Write down the system of equations. $\newline$ $2x + 3y = 5$ ...( $1$ ) $\newline$ $3x + 2y = 6$ ...( $2$ )
Multiply Equations: Multiply equation ( $1$ ) by $3$ and equation ( $2$ ) by $2$ to make the coefficients of $x$ the same. $\newline$ $3(2x + 3y) = 3\times5$ ...( $3$ ) $\newline$ $2(3x + 2y) = 2\times6$ ...( $4$ )
Perform Multiplication: Perform the multiplication. $\newline$ $6x + 9y = 15$ ...( $5$ ) $\newline$ $6x + 4y = 12$ ...( $6$ )
Eliminate x: Subtract equation $(6)$ from equation $(5)$ to eliminate x. $\newline$ $(6x + 9y) - (6x + 4y) = 15 - 12$
Simplify Equation: Simplify the equation. $\newline$ $6x - 6x + 9y - 4y = 15 - 12$ $\newline$ $0x + 5y = 3$ $\newline$ $5y = 3$
Solve for y: Solve for y. $\newline$ $y = \frac{3}{5}$
Substitute $y$ for $x$ : Substitute $y = \frac{3}{5}$ into equation ( $1$ ) to solve for $x$ . $2x + 3\left(\frac{3}{5}\right) = 5$
Perform Multiplication: Perform the multiplication. $2x + \frac{9}{5} = 5$
Combine Fractions: Convert $5$ to a fraction with a denominator of $5$ to combine with $\frac{9}{5}$ . $\newline$ $2x + \frac{9}{5} = \frac{25}{5}$
Subtract Fractions: Subtract $\frac{9}{5}$ from both sides. $\newline$ $2x = \frac{25}{5} - \frac{9}{5}$ $\newline$ $2x = \frac{16}{5}$
Solve for x: Solve for x. $\newline$ $x = \frac{16}{5} / 2$ $\newline$ $x = \frac{16}{5} \times \frac{1}{2}$ $\newline$ $x = \frac{16}{10}$ $\newline$ $x = \frac{8}{5}$