Multiply by -1.5: Multiply the second equation by a number that will allow us to eliminate one of the variables when we subtract one equation from the other. We can multiply the second equation by -1.5 to make the coefficients of y in both equations opposites. -1.5 * (2x + 4y) = -1.5 * 38 This gives us -3x - 6y = -57.Add to eliminate y: Add the new equation from Step 1 to the first equation to eliminate y. (3x + 5y) + (-3x - 6y) = 52 + (-57) This simplifies to -y = -5.Solve for y: Solve for y. To isolate y, we divide both sides by -1. -y / -1 = -5 / -1 This gives us y = 5.Substitute and solve for x: Substitute the value of y back into one of the original equations to solve for x. We can use the second equation: 2x + 4y = 38. Substitute y = 5 into the equation: 2x + 4(5) = 38. This simplifies to 2x + 20 = 38.Final step: Solve for x: Solve for x. Subtract 20 from both sides of the equation to isolate 2x. 2x + 20 - 20 = 38 - 20 This simplifies to 2x = 18. Now, divide both sides by 2 to solve for x. 2x / 2 = 18 / 2 This gives us x = 9.

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$3 x+5 y=52$ $\newline$ $2 x+4 y=38$

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Math Problems

Grade 7

Solve equations involving like terms

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3 x+5 y=52

\newline

2 x+4 y=38

Multiply by $-1.5$ : Multiply the second equation by a number that will allow us to eliminate one of the variables when we subtract one equation from the other. $\newline$ We can multiply the second equation by $-1.5$ to make the coefficients of $y$ in both equations opposites. $\newline$ $-1.5 \times (2x + 4y) = -1.5 \times 38$ $\newline$ This gives us $-3x - 6y = -57$ .
Add to eliminate y: Add the new equation from Step $1$ to the first equation to eliminate y. $\newline$ $(3x + 5y) + (-3x - 6y) = 52 + (-57)$ $\newline$ This simplifies to $-y = -5$ .
Solve for y: Solve for y. $\newline$ To isolate y, we divide both sides by \(-1＂). $\newline$ -y / \(-1 = $-5$ / $-1$ ＂) $\newline$ This gives us y = \(5＂).
Substitute and solve for $x$ : Substitute the value of $y$ back into one of the original equations to solve for $x$ . We can use the second equation: $2x + 4y = 38$ . Substitute $y = 5$ into the equation: $2x + 4(5) = 38$ . This simplifies to $2x + 20 = 38$ .
Final step: Solve for $x$ : Solve for $x$ . $\newline$ Subtract $20$ from both sides of the equation to isolate $2x$ . $\newline$ $2x + 20 - 20 = 38 - 20$ $\newline$ This simplifies to $2x = 18$ . $\newline$ Now, divide both sides by $2$ to solve for $x$ . $\newline$ $\frac{2x}{2} = \frac{18}{2}$ $\newline$ This gives us $x = 9$ .