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Solve this system of equations. Explain or show your reasoning.
y = -x + 9
y = 3x + 8

User Webmasters
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Final answer:

The solution to the system of equations y = -x + 9 and y = 3x + 8 is obtained by setting the two equations equal to each other, combining like terms, and solving for x first (x = 1/4) and then substituting that value into either original equation to find y (y = 35/4), resulting in the solution (1/4, 35/4).

Step-by-step explanation:

To solve the system of equations involving y = -x + 9 and y = 3x + 8, we can use the method of substitution or elimination. Both equations are structured to show y in terms of x, which means we can set them equal to each other since they both equal y:

-x + 9 = 3x + 8

Next, we combine like terms by adding x to both sides and subtracting 8 from both sides:

1 + 9 - 8 = 3x + x

Combining like terms, we get:

1 = 4x

Now, divide both sides by 4 to isolate x:

x = 1/4

Once we have x, we can substitute it back into either original equation to solve for y. Using y = -x + 9:

y = -(1/4) + 9

y = 9 - 1/4

y = 8.75 or y = 35/4

Therefore, the solution to the system of equations is (1/4, 35/4).

User Turiyag
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