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solve the system of equations. −7x−6y=4-7x - 6y = 4 and x=−3y+8x = -3y + 8

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Q. solve the system of equations. −7x−6y=4-7x - 6y = 4 and x=−3y+8x = -3y + 8
  1. Identify Equations: Identify the system of equations to be solved.\newlineThe system of equations given is:\newline−7x−6y=4-7x - 6y = 4\newlinex=−3y+8x = -3y + 8
  2. Substitute xx: Since the second equation is already solved for xx, we can substitute the expression for xx from the second equation into the first equation.\newlineSubstitute x=−3y+8x = -3y + 8 into the first equation:\newline−7(−3y+8)−6y=4-7(-3y + 8) - 6y = 4
  3. Distribute −7-7: Distribute −7-7 to the terms inside the parentheses in the first equation.\newline−7×−3y+−7×8−6y=4-7 \times -3y + -7 \times 8 - 6y = 4\newline21y−56−6y=421y - 56 - 6y = 4
  4. Combine Like Terms: Combine like terms in the first equation.\newline21y−6y=15y21y - 6y = 15y\newline15y−56=415y - 56 = 4
  5. Add 5656: Add 5656 to both sides of the equation to isolate the term with the variable yy.\newline15y−56+56=4+5615y - 56 + 56 = 4 + 56\newline15y=6015y = 60
  6. Divide by 1515: Divide both sides of the equation by 1515 to solve for yy.15y15=6015\frac{15y}{15} = \frac{60}{15}y=4y = 4
  7. Substitute yy: Now that we have the value of yy, we can substitute it back into the second equation to solve for xx.\newlineSubstitute y=4y = 4 into x=−3y+8x = -3y + 8:\newlinex=−3(4)+8x = -3(4) + 8
  8. Multiply and Add: Multiply −3-3 by 44 and add 88 to find the value of xx.\newlinex=−12+8x = -12 + 8\newlinex=−4x = -4

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