Question

Solve by elimination. y=3x+1 and -x+2y=-3

Answer 1

y = -8/7 and x = -5/7.

Explanation:

Step 1: Bring 3x from y = 3x + 1 to the left-hand side to make the equation similar to x + 2y = -3:

(y = 3x + 1) - 3x

-3x + y = 1

Step 2: Multiply the second equation by 3 and simplify:

We can multiply the second equation by 3, which will allow to solve for y by eliminating the xs since -3x + 3x = 0.

3(x + 2y = -3)

3x + 6y = -9

Step 3: Add -3x + y = 1 and 3x + 6y = -9 to eliminate x and solve for y

-3x + y = 1

+

3x + 6y = -9

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(-3x + 3x) + (y + 6y) = (1 - 9)

7y = -8

Step 4: Divide both sides by 7 to solve for y:

(7y = -8) / 7

y = -8/7

Thus, y = -8/7.

Step 5: Plug in -8/7 for y in y = 3x + 1 to solve for x:

-8/7 = 3x + 1

Step 6: Subtract 1 from both sides:

(-8/7 = 3x + 1) - 1

-15/7 = 3x

Step 7: Divide both sides by 3 to solve for x:

Note that since we're dividing a fraction, we'll end up multiplying by the reciprocal of 3 (i.e., 1/3) to solve for x:

(-15/7 = 3x) / 3

-15/7 = 3x) * 1/3

x = -5/7

Thus, x = -5/7.

Therefore, y = -8/7 and x = -5/7.

Answer 2

x = -1/8 and y = 5/8 OR x = -0.125 and y = 0.625

Explanation:

y = 3x + 1

x + 2y = -3

rearrange to line up variables:

3x - y = -1

x + 2y = -3

multiply the second equation by 3 so that the y values eliminate each other and then subtract them:

3x - y = -1

-

3x + 6y = -9

___________

0x + 5y = 8

solve for y:

5y = 8 --> y = 5/8

Plug in y to one of the equations to solve for x:

3x - 5/8 = -1

3x = -3/8

x = -3/24 = -1/8

therefore: x = -1/8 and y = 5/8 or x = -0.125 and y = 0.625