Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
(d1,w1)=(0,7)(d2,w2)=(141465,421)
Evaluate
{d=2×7w×3d2×7w×3d=15(7−w)
Calculate
More Steps

Evaluate
2×7×3
Multiply the terms
14×3
Multiply the numbers
42
{d=42wd2×7w×3d=15(7−w)
Calculate
More Steps

Evaluate
2×7×3
Multiply the terms
14×3
Multiply the numbers
42
{d=42wd42wd=15(7−w)
Solve the equation
More Steps

Evaluate
d=42wd
Move the expression to the left side
d−42wd=0
Factor the expression
d(1−42w)=0
Separate the equation into 2 possible cases
d=0∪1−42w=0
Solve the equation
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Evaluate
1−42w=0
Move the constant to the right-hand side and change its sign
−42w=0−1
Removing 0 doesn't change the value,so remove it from the expression
−42w=−1
Change the signs on both sides of the equation
42w=1
Divide both sides
4242w=421
Divide the numbers
w=421
d=0∪w=421
{d=0∪w=42142wd=15(7−w)
Evaluate
{d=042wd=15(7−w)∪{w=42142wd=15(7−w)
Calculate
More Steps

Evaluate
{d=042wd=15(7−w)
Substitute the given value of d into the equation 42wd=15(7−w)
42w×0=15(7−w)
Any expression multiplied by 0 equals 0
0=15(7−w)
Swap the sides of the equation
15(7−w)=0
Rewrite the expression
7−w=0
Move the constant to the right side
−w=0−7
Removing 0 doesn't change the value,so remove it from the expression
−w=−7
Change the signs on both sides of the equation
w=7
Calculate
{d=0w=7
{d=0w=7∪{w=42142wd=15(7−w)
Calculate
More Steps

Evaluate
{w=42142wd=15(7−w)
Substitute the given value of w into the equation 42wd=15(7−w)
42×421d=15(7−421)
Simplify
d=15(7−421)
Simplify
More Steps

Evaluate
15(7−421)
Subtract the numbers
15×42293
Reduce the numbers
5×14293
Multiply the numbers
145×293
Multiply the numbers
141465
d=141465
Calculate
{d=141465w=421
{d=0w=7∪{d=141465w=421
Check the solution
More Steps

Check the solution
{0=2(7×7)×3×02(7×7)×3×0=15(7−7)
Simplify
{0=00=0
Evaluate
true
{d=0w=7∪{d=141465w=421
Check the solution
More Steps

Check the solution
{141465=2(7×421)×3×1414652(7×421)×3×141465=15(7−421)
Simplify
{104.64˙28571˙=104.64˙28571˙104.64˙28571˙=104.64˙28571˙
Evaluate
true
{d=0w=7∪{d=141465w=421
Solution
(d1,w1)=(0,7)(d2,w2)=(141465,421)
Show Solution
