Step 1) Because the first equation is already solved for yy we can substitute (4x - 13)(4x−13) for yy in the second equation and solve for xx:
31x - 6y = 2931x−6y=29 becomes:
31x - 6(4x - 13) = 2931x−6(4x−13)=29
31x - (6 * 4x) + (6 * 13) = 2931x−(6⋅4x)+(6⋅13)=29
31x - 24x + 78 = 2931x−24x+78=29
(31 - 24)x + 78 = 29(31−24)x+78=29
7x + 78 = 297x+78=29
7x + 78 - color(red)(78) = 29 - color(red)(78)7x+78−78=29−78
7x - 0 = -497x−0=−49
7x = -497x=−49
(7x)/color(red)(7) = -49/color(red)(7)7x7=−497
(color(red)(cancel(color(black)(7)))x)/cancel(color(red)(7)) = -7
x = -7
Step 2) Substitute -7 for x in the first equation and calculate y:
y = 4x - 13 becomes:
y = (4 xx -7) - 13
y = -28 - 13
y = -41
The Solution Is: x = -7 and y = -41 or (-7, -41)
