Solving by elimination and substitution:
#x+y = 7#
#2x-y = 2#
on adding the two equations #y# gets cancelled
#x + cancel(y) = 7#
#2x - cancel(y) = 2#
#3x = 9#
# x = 9/3 = 3#
substituting this value of #x# in equation 1:
#x + y = 7#
# 3+ y = 7#
# y = 7- 3#
#y = 4#
the solution for the system of equations are :
#color(blue)x=3#
#color(blue)y=4#
See a solution process below:
Step 1) Solve the second equation for #y#:
#-x + y = -4#
#-x + color(red)(x) + y = -4 + color(red)(x)#
#0 + y = -4 + x#
#y = -4 + x#
Step 2) Substitute #(-4 + x)# for #y# in the first equation and solve for #x# :
#2x - y = 7# becomes:
#2x - (-4 + x) = 7#
#2x + 4 - x = 7#
#2x - x + 4 = 7#
#2x - 1x + 4 = 7#
#(2 - 1)x + 4 = 7#
#1x + 4 = 7#
#x + 4 = 7#
#x + 4 - color(red)(4) = 7 - color(red)(4)#
#x + 0 = 3#
#x = 3#
Step 3) Substitute #3# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#:
#y = -4 + x# becomes:
#y = -4 + 3x#
#y = -1#
The Solution Is:
#x = 3# and #y = -1#
Or
#(3, -1)#
2, x, minus, y, equals, 7
Solve for x
x=\frac{y+7}{2}
Solve for y
y=2x-7
Graph
Quiz
Linear Equation
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2x=7+y
Add y to both sides.
2x=y+7
The equation is in standard form.
\frac{2x}{2}=\frac{y+7}{2}
Divide both sides by 2.
x=\frac{y+7}{2}
Dividing by 2 undoes the multiplication by 2.
-y=7-2x
Subtract 2x from both sides.
\frac{-y}{-1}=\frac{7-2x}{-1}
Divide both sides by -1.
y=\frac{7-2x}{-1}
Dividing by -1 undoes the multiplication by -1.
y=2x-7
Divide 7-2x by -1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}
Solution:
2x - y = 7 …. (1)
y = 2x + 3 …. (2)
Let us use the substitution method to solve the system of linear equations
Substituting equation (2) in (1)
2x - (2x + 3) = 7
By further calculation
2x - 2x - 3 = 7
-3 = 7
Therefore, there is no solution.
What is the solution to the system of equations? 2x - y = 7 and y = 2x + 3
Summary:
The system of equations 2x - y = 7 and y = 2x + 3 has no solution.
Math worksheets and
visual curriculum
Solution:
The equations of degree 1 is called linear equations. The standard form of linear equations in two variables is ax + by = c, where a, b and c are constants.
To solve the system of linear equations we will substitute the value of y.
Let 2x – y = 7 be equation (1) and y = 2x + 3 be equation (2)
Put the value of y = 2x + 3 in equation (1).
⇒ 2 x – ( 2x + 3 ) = 7
⇒ 2x - 2x - 3 = 7
⇒ - 3 = 7
So, there is no solution.
We can use Cuemath's online system of equations calculator to solve the equations.
Thus, the system of linear equations 2x – y = 7 and y = 2x + 3, has no solution.
What is the solution to the system of equations 2x - y = 7, y = 2x + 3?
Summary:
The system of linear equations 2x - y = 7, and y = 2x + 3, has no solution.