How do you solve 35x - 5y = 20 and y = 7x + 4 using substitution?

2 Answers
smendyka
Aug 30, 2017

See a solution process below:

Explanation:

Step 1) Because the second equation is already solved for y we can substitute (7x + 4) for y in the first equation and solve for x:

35x - 5y = 20 becomes:

35x - 5(7x + 4) = 20

35x - (5 * 7x) - (5 * 4) = 20

35x - 35x - 20 = 20

35x - 35x - 20 = 20

0 - 20 = 20

-20 != 20

This indicates there are no solutions to this system of equations. Or, no solution set is the empty or null set: {O/}

This also indicates, if there is no solutions, that these equations represent parallel lines.

SCooke
Aug 30, 2017

"Substitute" the expression for y in the second equation into the first one.

Explanation:

35x − 5(7x + 4) = 20
35x − 35x - 20 = 20
0 = 40
0 does not = 40, so there is no solution to this set.

Converting both to slope-intercept form gives us:
35x − 5y = 20 ; -5y = -35x + 20 Dividing by -5 we get:
y = 7x - 4; compared to the second equation
y = 7x + 4

They are parallel lines (same slope) with different intercepts (4 and -4).

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