Write Equations: Write down the given system of equations. We have two equations: 1) y = -3x + 5 2) 5x - 4y = -3Substitute y: Substitute the expression for y from the first equation into the second equation. Since y = -3x + 5, we can replace y in the second equation with -3x + 5. So, 5x - 4(-3x + 5) = -3 becomes our new equation.Distribute -4: Distribute the -4 across the parentheses in the new equation. 5x - 4(-3x) + 4(5) = -3 This simplifies to: 5x + 12x - 20 = -3Combine Like Terms: Combine like terms on the left side of the equation. 5x + 12x = 17x So, 17x - 20 = -3Add 20: Add 20 to both sides of the equation to isolate the term with x. 17x - 20 + 20 = -3 + 20 This simplifies to: 17x = 17Divide by 17: Divide both sides of the equation by 17 to solve for x. 17x / 17 = 17 / 17 This gives us: x = 1Substitute x: Substitute the value of x back into the first equation to solve for y. y = -3(1) + 5 This simplifies to: y = -3 + 5Calculate y: Calculate the value of y. y = 2

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$y=-3x+5$ $\newline$ $5x-4y=-3$

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Math Problems

Grade 7

Solve equations involving like terms

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y=-3x+5

\newline

5x-4y=-3

Write Equations: Write down the given system of equations. $\newline$ We have two equations: $\newline$ $1$ ) $y = -3x + 5$ $\newline$ $2$ ) $5x - 4y = -3$
Substitute $y$ : Substitute the expression for $y$ from the first equation into the second equation. $\newline$ Since $y = -3x + 5$ , we can replace $y$ in the second equation with $-3x + 5$ . $\newline$ So, $5x - 4(-3x + 5) = -3$ becomes our new equation.
Distribute $-4$ : Distribute the $-4$ across the parentheses in the new equation. $5x - 4(-3x) + 4(5) = -3$ This simplifies to: $5x + 12x - 20 = -3$
Combine Like Terms: Combine like terms on the left side of the equation. $\newline$ $5x + 12x = 17x$ $\newline$ So, $17x - 20 = -3$
Add $20$ : Add $20$ to both sides of the equation to isolate the term with $x$ . $\newline$ $17x - 20 + 20 = -3 + 20$ $\newline$ This simplifies to: $\newline$ $17x = 17$
Divide by $17$ : Divide both sides of the equation by $17$ to solve for $x$ . $\frac{17x}{17} = \frac{17}{17}$ This gives us: $x = 1$
Substitute $x$ : Substitute the value of $x$ back into the first equation to solve for $y$ . $\newline$ $y = -3(1) + 5$ $\newline$ This simplifies to: $\newline$ $y = -3 + 5$
Calculate $y$ : Calculate the value of $y$ . $y = 2$