Question

Solve the system of linear equations by substitution.

Answer 1

Answer: The solution is the ordered pair (1/2,  -3/4) so x = 1/2 and y = -3/4 pair up together. The two lines, when graphed, cross at this location.

note: 1/2 = 0.5 and -3/4 = -0.75; so the intersection point can be written as (0.5, -0.75)

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Explanation:

The second equation has y isolated. We can replace the y in the first equation with the expression 1/2x - 1

3x + 2y = 0

3x + 2( y ) = 0

3x + 2( 1/2x - 1) = 0 ... y is replaced with 1/2x-1

3x + 2(1/2x) + 2(-1) = 0 .... distribute

3x + x - 2 = 0 .... note how 2 times 1/2 is 1

4x - 2 = 0

4x = 2

x = 2/4

x = 1/2

Use this x value to find the y value it pairs with

y = (1/2)*x - 1

y = (1/2)*(1/2) - 1 ... replace x with 1/2

y = 1/4 - 1

y = 1/4 - 4/4

y = (1-4)/4

y = -3/4