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Solve the system by substitution. {:[x=-3y+7],[-4x-5y=7]:}

Solve the system by substitution.\newlinex=−3y+7−4x−5y=7 \begin{aligned} x & =-3 y+7 \\ -4 x-5 y & =7 \end{aligned}

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Q. Solve the system by substitution.\newlinex=−3y+7−4x−5y=7 \begin{aligned} x & =-3 y+7 \\ -4 x-5 y & =7 \end{aligned}
  1. Substitute xx in second equation: Substitute the expression for xx from the first equation into the second equation.\newlineGiven the first equation x=−3y+7x = -3y + 7, we can substitute this into the second equation −4x−5y=7-4x - 5y = 7.
  2. Perform substitution: Perform the substitution.\newlineSubstitute x=−3y+7x = -3y + 7 into −4x−5y=7-4x - 5y = 7.\newline−4(−3y+7)−5y=7-4(-3y + 7) - 5y = 7
  3. Distribute and simplify: Distribute −4-4 across the terms in the parentheses.\newline−4×−3y+−4×7−5y=7-4 \times -3y + -4 \times 7 - 5y = 7\newline12y−28−5y=712y - 28 - 5y = 7
  4. Combine like terms: Combine like terms. \newline12y−5y−28=712y - 5y - 28 = 7\newline7y−28=77y - 28 = 7
  5. Isolate y term: Add 2828 to both sides of the equation to isolate the term with yy.\newline7y−28+28=7+287y - 28 + 28 = 7 + 28\newline7y=357y = 35
  6. Solve for y: Divide both sides by 77 to solve for y.\newline7y7=357\frac{7y}{7} = \frac{35}{7}\newliney=5y = 5
  7. Substitute yy in first equation: Substitute the value of yy back into the first equation to solve for xx.x=−3y+7x = -3y + 7x=−3(5)+7x = -3(5) + 7
  8. Calculate xx: Perform the calculation to find the value of xx.x=−15+7x = -15 + 7x=−8x = -8
  9. Write solution as ordered pair: Write the solution as an ordered pair (x,y)(x, y).\newlineThe solution is (−8,5)(-8, 5).

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