Is there another way of solving this without subtraction?

Question

2x + y = 7
-5x + 5y = -40

Answer 1

substitution
solve 1st equation for y
y=-2x+7 and put that into the 2nd
-5x +5(-2x+7)=-40
and solve that for x

then put that answer into y = -2x+7 to get the y

Answer 2

yes i think the first procedure is solving it by the crammers rule.
the second rule is plot the graph with two straigh lines using these equations and the intersection point is the answer.
the third is,

y=7-2x

-5x+5(7-2x) = -40
=> -5x+35-10x = -40
=> -15x+35 = -40
=> -15x = -75
=> x= 5;

so, y=7-2x
=> y=7-2(5);
=> y=7-10;
=> y= -3;
thats the answer

Answer 3

Let

2x + y = 7 (equation 1)

-5x + 5y = -40 (equation 2)

equation 2 can be simplified by dividing both sides with 5, to yield

-x+y= -8 (equation 3)

We can multiply equation 3 by 2 to yield

-2x+2y=-16 (equation 4)

We can then add equations 4 and 1 together.

2x-2x +2y +y =-16+7

3y =-9

y=- 3 substituting this into equation 1 yields

x=(7-y)/2 = (7+3)/2 = 10/2=5

Answer 4

2x+y=7 so,y=7-2x

-5x+5y=-40 sub y=7-2x in this

so,-5x+35-10x=-40
-15x+35=-40
-15x=-75
x=5
sub this in 2x+y=7
10+y=7
y= -3

x=5 y= -3

Answer 5

2x + y = 7 (Eq. 1)

-5x +5y = -40 (Eq.2)

Multiply Eq.1 by 5

10x + 5y = 35 (Eq.3) i.e. 5y = 35 - 10x

Sub Eq.3 into Eq.2 for y

-5x + 35 - 10x = -40
- 15x = -75
x = 5

Sub back into Eq.1

2x + y = 7
10 + y = 7
y = 7 - 10 = -3

Y = -3 x = 5

Answer 6

solve the 1st equation for y

y=-2x+7

sub into the 2nd equation

-5x+5*(-2x)+5*7=-40
-5x-10x+35=-40
-15x=-75
x=5

sub back into the 1st equation

2*5+y=7
y=-3

Answer 7

Yes, by Cramers rule. You also can solve it by plotting graph for two lines. The point of intersection is the solution.

Answer 8

You can do it with linear algebra, too.
[A]{B}={C}
{B}=[A]^-1{C}
Where the matrices are as follows:

A= 2 1
-5 5

B= X
Y

C= 7
-40

Just invert [A] and multiply it by {C}. If you don't remember how to invert [A], look it up...it's not just flipping it...