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Find the solution to the system of equations. $y= -5x + 6$ and $y= 3x - 2$

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Solve polynomial equations

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Q. Find the solution to the system of equations.

y= -5x + 6

and

y= 3x - 2

Set Equations Equal: To find the solution to the system of equations, we need to set the two equations equal to each other since they both equal $y$ . $y = -5x + 6$ $y = 3x - 2$ So, $-5x + 6 = 3x - 2$
Solve for x: Now, we will solve for $x$ by moving all terms involving $x$ to one side and the constant terms to the other side. $-5x - 3x = -2 - 6$
Combine Like Terms: Combine like terms to simplify the equation. $\newline$ $-8x = -8$
Divide to Solve $x$ : Divide both sides by $-8$ to solve for $x$ . $x = \frac{-8}{-8}$
Substitute $x$ Value: Simplify the fraction to find the value of $x$ . $x = 1$
Solve for y: Now that we have the value of $x$ , we can substitute it back into either of the original equations to solve for $y$ . We'll use the first equation $y = -5x + 6$ . $\newline$ $y = -5(1) + 6$
Perform Multiplication: Perform the multiplication and addition to solve for $y$ . $y = -5 + 6$
Combine Numbers: Combine the numbers to find the value of $y$ . $y = 1$

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