Question

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Question

What values of x

and y

satisfy the system {y=−2x+3
y=5x−4?


Enter your answer as an ordered pair, like this: (42, 53)


If your answer includes one or more fractions, use the / symbol to separate numerators and denominators. For example, if your answer is (4253,6475),

enter it like this: (42/53, 64/75)


If there is no solution, enter "no"; if there are infinitely many solutions, enter "inf."

Answer 1

Answer as an ordered pair: (1, 1)

Explanation:

Method to solve: Elimination:

First we need to multiply the first equation by -1. Then, we'll add the two equations to eliminate the ys and solve for x:

Multiplying y = -2x + 3 by -1:

-1(y = -2x + 3)

-y = 2x - 3

Adding -y = 2x - 3 and y = 5x - 4:

-y = 2x - 3

+

y = 5x - 4

----------------------------------------------------------------------------------------------------------

(-y + y) = (2x + 5x) + (-3 - 4)

Solving for x:

(0 = 7x - 7) + 7

(7 = 7x) / 7

1 = x

Thus, x = 1. Now we can solve for y by plugging in 1 for x in any of the two equations in the system. Let's use the first one:

Plugging in 1 for x in y = -2x + 3:

y = -2(1) + 3

y = -2 + 3

y = 1

Thus, y = 1

Therefore, the answer as an ordered pair is (1, 1)

Optional Step: Checking the validity of our answers:

Now we can check that our answers are correct by plugging in (1, 1) for (x, y) in both equations and seeing if we get the same answers on both sides of the equation:

Plugging in 1 for x and 1 for y in y = -2x + 3:

1 = -2(1) + 3

1 = -2 + 3

1 = 1

Plugging in 1 for x and 1 for y in y = 5x - 4:

1 = 5(1) - 4

1 = 5 - 4

1 = 1

Thus, our answers are correct.