Solve. -5x+4y=3 x=2y-15

Write System of Equations: First, we have the system of equations: 1) -5x + 4y = 3 2) x = 2y - 15 We will use the substitution method to solve for x and y. Since the second equation gives us x in terms of y, we can substitute x in the first equation with the expression from the second equation.Substitute x in First Equation: Substitute x from the second equation into the first equation: -5(2y - 15) + 4y = 3 Now, distribute the -5 into the parentheses.Perform Distribution: Perform the distribution: -10y + 75 + 4y = 3 Now, combine like terms.Combine Like Terms: Combine the y terms: -10y + 4y = -6y So, the equation becomes: -6y + 75 = 3 Now, we will isolate the y term by moving the constant to the other side.Isolate y Term: Subtract 75 from both sides of the equation: -6y + 75 - 75 = 3 - 75 This simplifies to: -6y = -72 Now, divide both sides by -6 to solve for y.Divide by -6 for y: Divide both sides by -6: y = -72 / -6 This simplifies to: y = 12 We have found the value of y. Now we will substitute this value back into the second equation to find x.Substitute y in Second Equation: Substitute y = 12 into the second equation: x = 2(12) - 15 Now, perform the multiplication and subtraction.Calculate x Value: Calculate the value of x: x = 24 - 15 This simplifies to: x = 9 We have now found the values of both x and y.

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Solve. $\newline$ - $5x+4y=3$ $\newline$ $x=2y-15$

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Algebra 1

Solve linear equations with variables on both sides

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Q. Solve.

\newline

5x+4y=3

\newline

x=2y-15

Write System of Equations: First, we have the system of equations: $\newline$ $1$ ) $-5x + 4y = 3$ $\newline$ $2$ ) $x = 2y - 15$ $\newline$ We will use the substitution method to solve for $x$ and $y$ . Since the second equation gives us $x$ in terms of $y$ , we can substitute $x$ in the first equation with the expression from the second equation.
Substitute $x$ in First Equation: Substitute $x$ from the second equation into the first equation: $\newline$ $-5(2y - 15) + 4y = 3$ $\newline$ Now, distribute the $-5$ into the parentheses.
Perform Distribution: Perform the distribution: $\newline$ $-10y + 75 + 4y = 3$ $\newline$ Now, combine like terms.
Combine Like Terms: Combine the $y$ terms: $\newline$ $-10y + 4y = -6y$ $\newline$ So, the equation becomes: $\newline$ $-6y + 75 = 3$ $\newline$ Now, we will isolate the $y$ term by moving the constant to the other side.
Isolate y Term: Subtract $75$ from both sides of the equation: $\newline$ $-6y + 75 - 75 = 3 - 75$ $\newline$ This simplifies to: $\newline$ $-6y = -72$ $\newline$ Now, divide both sides by $-6$ to solve for $y$ .
Divide by $-6$ for $y$ : Divide both sides by $-6$ : $\newline$ $y = \frac{-72}{-6}$ $\newline$ This simplifies to: $\newline$ $y = 12$ $\newline$ We have found the value of $y$ . Now we will substitute this value back into the second equation to find $x$ .
Substitute $y$ in Second Equation: Substitute $y = 12$ into the second equation: $\newline$ $x = 2(12) - 15$ $\newline$ Now, perform the multiplication and subtraction.
Calculate x Value: Calculate the value of x: $\newline$ $x = 24 - 15$ $\newline$ This simplifies to: $\newline$ $x = 9$ $\newline$ We have now found the values of both $x$ and $y$ .