Solve the system of equations. {:[-5x+4y=3],[x=2y-15],[x=◻],[y=◻]:}

Solve for x: Solve the second equation for x. The second equation is x = 2y - 15. We can use this expression for x to substitute into the first equation.Substitute x into first equation: Substitute x = 2y - 15 into the first equation. The first equation is -5x + 4y = 3. Replace x with 2y - 15 to get: -5(2y - 15) + 4y = 3Distribute and combine like terms: Distribute -5 and combine like terms. -10y + 75 + 4y = 3 -6y + 75 = 3Isolate the variable y: Isolate the variable y. Subtract 75 from both sides of the equation to get: -6y = 3 - 75 -6y = -72Solve for y: Solve for y. Divide both sides by -6 to find the value of y: y = -72 / -6 y = 12Substitute y into second equation: Substitute y = 12 into the second equation to find x. The second equation is x = 2y - 15. Substitute y with 12: x = 2(12) - 15 x = 24 - 15 x = 9Check the solution: Check the solution in the first equation. Substitute x = 9 and y = 12 into the first equation -5x + 4y = 3: -5(9) + 4(12) = 3 -45 + 48 = 3 3 = 3 The left side equals the right side, so the solution checks out.

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Solve the system of equations.

{:[-5x+4y=3],[x=2y-15],[x=◻],[y=◻]:}

Solve the system of equations. $\newline$ $\begin{array}{l} -5 x+4 y=3 \\ x=2 y-15 \\ x=\square \\ y=\square \end{array}$

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Math Problems

Algebra 1

Solve a system of equations using substitution

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Q. Solve the system of equations.

\newline

\begin{array}{l} -5 x+4 y=3 \\ x=2 y-15 \\ x=\square \\ y=\square \end{array}

Solve for x: Solve the second equation for x. $\newline$ The second equation is $x = 2y - 15$ . We can use this expression for $x$ to substitute into the first equation.
Substitute $x$ into first equation: Substitute $x = 2y - 15$ into the first equation. $\newline$ The first equation is $-5x + 4y = 3$ . Replace $x$ with $2y - 15$ to get: $\newline$ $-5(2y - 15) + 4y = 3$
Distribute and combine like terms: Distribute $-5$ and combine like terms. $\newline$ $-10y + 75 + 4y = 3$ $\newline$ $-6y + 75 = 3$
Isolate the variable y: Isolate the variable y. $\newline$ Subtract $75$ from both sides of the equation to get: $\newline$ $-6y = 3 - 75$ $\newline$ $-6y = -72$
Solve for y: Solve for y. $\newline$ Divide both sides by $-6$ to find the value of y: $\newline$ $y = \frac{-72}{-6}$ $\newline$ $y = 12$
Substitute $y$ into second equation: Substitute $y = 12$ into the second equation to find $x$ . $\newline$ The second equation is $x = 2y - 15$ . Substitute $y$ with $12$ : $\newline$ $x = 2(12) - 15$ $\newline$ $x = 24 - 15$ $\newline$ $x = 9$
Check the solution: Check the solution in the first equation. $\newline$ Substitute $x = 9$ and $y = 12$ into the first equation $-5x + 4y = 3$ : $\newline$ $-5(9) + 4(12) = 3$ $\newline$ $-45 + 48 = 3$ $\newline$ $3 = 3$ $\newline$ The left side equals the right side, so the solution checks out.