Algebra
Calculus
Trigonometry
Matrix
Question
Solve the system of equations
Solve using the substitution method
Solve using the elimination method
Solve using the Gauss-Jordan method
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(x,y)=(3,1)
Evaluate
{2x+y=72x−3y=3
Solve the equation for y
{y=7−2x2x−3y=3
Substitute the given value of y into the equation 2x−3y=3
2x−3(7−2x)=3
Simplify
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Evaluate
2x−3(7−2x)
Expand the expression
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Calculate
−3(7−2x)
Apply the distributive property
−3×7−(−3×2x)
Multiply the numbers
−21−(−3×2x)
Multiply the numbers
−21−(−6x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−21+6x
2x−21+6x
Add the terms
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Evaluate
2x+6x
Collect like terms by calculating the sum or difference of their coefficients
(2+6)x
Add the numbers
8x
8x−21
8x−21=3
Move the constant to the right-hand side and change its sign
8x=3+21
Add the numbers
8x=24
Divide both sides
88x=824
Divide the numbers
x=824
Divide the numbers
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Evaluate
824
Reduce the numbers
13
Calculate
3
x=3
Substitute the given value of x into the equation y=7−2x
y=7−2×3
Calculate
y=1
Calculate
{x=3y=1
Check the solution
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Check the solution
{2×3+1=72×3−3×1=3
Simplify
{7=73=3
Evaluate
true
{x=3y=1
Solution
(x,y)=(3,1)
Show Solution
Relationship between lines
Neither parallel nor perpendicular
Evaluate
2x+y=7,2x−3y=3
Write the equation in slope-intercept form
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Evaluate
2x+y=7
Move the expression to the right side
y=7−2x
Rearrange the terms
y=−2x+7
y=−2x+7,2x−3y=3
Write the equation in slope-intercept form
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Evaluate
2x−3y=3
Move the expression to the right side
−3y=3−2x
Divide both sides
y=−1+32x
Rearrange the terms
y=32x−1
y=−2x+7,y=32x−1
Since the line is in slope-intercept form, the coefficient −2 is the slope of the line
−2,y=32x−1
Since the line is in slope-intercept form, the coefficient 32 is the slope of the line
−2,32
The slopes are different, so the lines aren't parallel. We'll multiply the slopes to check their relationship
−2×32
Multiply the numbers
−32×2
Multiply the numbers
−34
Solution
Neither parallel nor perpendicular
Show Solution
Graph
